# Algebraic expressions: definition, formulas, example (2023)

• Written byPriya_Singh Algebraic Expressions: Algebraic expressions are used to calculate solutions to any mathematical operation involving variables such as addition, subtraction, multiplication or division. There are three types of algebraic expressions; monomial expression, binomial expression and polynomial expression. In addition, Boolean algebra plays an important role in algebraic expressions.

An unknown value is represented as the letters x, y, and z in the basics of algebraic expressions. These letters are called variables. An algebraic expression can have both variables and constants. Together they form the algebraic expression. In this article, we will learn about algebraic expressions and Boolean algebra in detail.

## Definition of algebraic expressions for Boolean algebra

Many students wonder what exactly algebraic expressions are, or what isDefinition of algebraic expressions. So here is the answer: The combination of the constants and variables generated by some or all of the four basic operations addition (( + ),) subtraction (( – ),) multiplication ((times)) and division (( ÷ )) is called known algebraic expression.

Examples:(4x+5,10y – 5) are examples of the algebraic expression.

### Algebraic constant

The constant meaning in mathematics is as follows:

Any quantity whose value never changes in the given topic (or range) of discussion is called a constant.

Example: (2,6,115,pi,e,……) are constants.

### Algebraic Variable

The meaning of variables in mathematics is as follows:

Any quantity whose value changes in the given topic (or scope) of discussion is called a variable.

Example: Traditionally (x,y,z...) are used as variables.

(Video) Definition of expression, algebraic expression and equation in maths with examples / Amir maths tuto

note:Usually the lower case letters (x,y,z...) are used as variables and (a,b,c,p,q,r,.....) as constants. But sometimes the letters (a,b,c,p,q,r,…..) are also used as variables. Therefore, it is advisable to mention in some cases which letter is used as a variable and which letter is used as a constant.

### Terms of algebraic expressions by Boolean algebra

In an algebraic expression, an expression consisting of $$(i)$$ only constant, $$(ii)$$ only one variable, $$(iii)$$ product of two or more variables, $$(iv)$$ a product of both the variable $$(s)$$ and the constant part. The terms can be positive or negative.

Beispiel: (4, 17, x, y, xy, yz, 5xyz, 12xy, -4, -17, -x, -y, -xy, – yz, -5xyz, -12xy,…) sind Terme.

#### coefficients

The fixed (or constant) number part, together with the sign (positive or negative) associated with each algebraic term, is called its coefficient.

Example: In the term (12xyz), the coefficient is (12).

In the term (-yz), the coefficient is (-1).

In the term (17), the coefficient is (17).

In the term (-4), the coefficient is (-4).

The degree of the polynomial is the highest integer power of the variables of its terms when the polynomial is expressed in its standard form. It is the sum of the exponents of the variables in the expression when there is more than one variable.

Examples: ({x^3}y + {x^2} + y + 13)
({x^3}y) has degree (4) ((3) for (x) and (1) for (y))
({x^2}) has degree (2)
The constant term (17) has degree (0).
So the highest degree among the three terms is (4). Hence the polynomial is said to have degree (4).

### Algebraic expressions and equations

An algebraic expression can contain one or more terms.

(I). If it contains a term, then it can only be a constant term or a term made up of constants and variables.

Example: (4, 17,- 4, -17, xy, -3yz,...) are each algebraic expressions with only one term.

(ii). If the algebraic expression contains more than one term, the different terms of the expression need only be separated by the (+) or (\) sign.

Beispiel: (4x + 5, 10y – 20, 3{x^2} + 2y – 5, xy+ x – y – 17,…)

### Types of algebraic expressions

Below we have provided the 3 main types of algebraic expressions:

(i) Based on the number of terms included
(ii) Based on the highest degree of terms
(iii) Based on the number of variables it contains.

(Video) ALGEBRAIC EXPRESSIONS Basic ( Definition , Terms , Factors , Coefficient )

### Algebraic expressions and equations based on number of terms

The differentalgebraic expressions and equationsbased on a number of terms are as follows:

1.Monomial: It is an algebraic expression that contains only one term.
Example: (5x, 2xy, – 3{a^2}b, – 7) etc. are monomials.
2. Binomial: An algebraic expression containing two terms is called a binomial.
Example: ((2a+3b),(8 – 3x),({x^2} – 4x{y^2})) etc. are binomials.
3.Trinomial: An algebraic expression containing three terms is called a trinomial.
Example: ((a, + 2b + 5c), (x + 2y – 3z), ({x^3} – {y^3} – {z^3})) etc. are trinominals.
4.Quadrinome: An algebraic expression that contains four terms is called a quadrinomial.
Example: ((x + y + z – 5), ({x^3} + {y^3} + {z^3} + 3xyz)) etc. are quadrinominals.
5.Polynomials: An expression containing two or more terms is called a polynomial. It includes binomials, trinomials, quadrinomials, and all algebraic expressions with five or more terms.

#### Algebraic expressions based on the highest degree of terms

The various algebraic expressions based on the highest degree of terms are as follows:

1.First degree: It is an algebraic expression with degree (1).
Example: (5x,x,y,...)etc.

2.Second Degree: It is an algebraic expression of degree (2).
Example: (5{x^2}, {x^2} + 3xy + 12{y^2} + 3x – 8y + 9,...)etc.

3.Third degree: It is an algebraic expression with degree (3).
Example: (5{x^3},{x^3} + 3xy + 12{y^2}, {y^2} + 3x – 8{y^3} + 9…)etc.

Etc.

#### Algebraic expressions based on the number of variables contained

The various algebraic expressions based on the number of variables included are as follows:

1.With one variable: It is an algebraic expression with only one variable.
Example: (5x, x+2, y – 9,...) etc.

2.With two variables: It is an algebraic expression with only two variables.
Example: (7xy, 5{x^2}+z, {x^2}+3xy + 12{y^2}, {y^2}+3x – 8y + 9,...), etc.

3.With three variables: It is an algebraic expression with only three variables.
Example: (6xyz,5{x^3} + 3y + z, {x^3} + 3xy + 12{y^2}z,{y^2} + 3xz – 8{y^3} + 9,... )

Etc.

### Like and contrary to terms

Students can learn about like and unlike terms in an algebraic expression worksheet below:

(I)Same term: The terms with the same algebraic factors are called similar terms.

(ii)Unlike term: The terms with different algebraic factors are called unlike terms.

Example: In the expression (2xy – 3x + 5xy – 4,) the terms (2xy) and (5xy) are equal terms because they have the same algebraic factors (xy) but the terms are (2xy) and (-3x). not equal to terms because they have different algebraic factors (xy) and (x) respectively.

(Video) Algebraic Expressions Definition class 8, Algebraic expressions definition in urdu

### Arithmetic operations on algebraic expressions

The arithmetic operationsAlgebraic expression worksheetsare given below:

In addition to the algebraic expression, equal terms are only added with equal terms. Coefficients of equal terms are added. Unlike terms, any terms remain associated with the result with whatever mathematical operator they have.

Example: (3x + 5y + z + 7 + 4x + 9y + 11)/( = 3x + 4x + 5y + 9y + z + 7 + 11) write the same terms together, there is no other similar term for (z) so, (= 7x, + 14y + z + 18) Add all pairs of equal terms and combine the respective results with their respective signs.

#### Subtraction of algebraic expressions

To subtract one algebraic expression from another, change the signs (from(+{rm{to} {rm{ – }} ,{rm{or}}, {rm{from}}, {rm{ – to} } ,{ rm{ + }})) of all terms of the expressions to be subtracted and then the two expressions are added according to the addition rules.

Example: Subtract (( – 2{y^2} + frac{1}{2}y – 3)from,7{y^2} – 2y + 10)

This is done as follows: ((7{y^2} – 2y + 10) – left( { – 2{y^2} + frac{1}{2}y + 3} right))
= 7{y^2} – 2y + 10 + 2{y^2} – frac{1}{2}y + 3)
= 7{y^2} + 2{y^2} – 2y – frac{1}{2}y + 10 + 3) (group like terms)
= (7 + 2){y^2} + left( { – 2 – frac{1}{2}} right)y + 13)
= 9{y^2} – frac{5}{2}y + 13)

#### Multiplication of algebraic expressions

General rule:

1. The product of two factors with the same sign is positive and the product of two factors with different signs is negative.
d.h. (( + ) mal ( + ) = + )
(( + ) mal ( – ) = – )
(( – ) mal ( + ) = – )
and (( – ) \times ( – ) = + )
2. If (a) is any variable and (m,n) are positive integers then ({a^m} times {a^n} = {a^{m + n}})
Beige: ({a^3},bad {a^5} = {a^{3 + 5}} = {a^8},{y^4}bad y = {y^{4 + 1}} = {y^5}) usw.

We have the following cases for multiplication:

#### Multiplication of two monomials

In this case, multiply the coefficient by the coefficient and the variable part by the variable part of the two monomials.
Example: (3ab times 5b = (3 times 5) times (ab times b) = 15a{b^2})

#### Multiplication of a monomial and a binomial

In this case, obey the distribution law of multiplication over addition (a times (b + c) = a times b + a times c)

Example: (3x(4{x^2} + y + 2z) = 3x times 4{x^2} + 3x times y + 3x times 2z = 12{x^3} + 3xy + 6zx)

#### Multiplication of two binomials

In this case we follow the rule $$(a + b) \times (c + d) = a \times (c + d) + b \times (c + d)$$ and then follow the rule of multiplying a binomial with a monomial.

Example:
((3x + 2)(4{x^2} + y) = 3x wrong (4{x^2} + y) + 2 wrong (4{x^2} + y))
( = 3x mal 4{x^2} + 3x mal y + 2 mal 4{x^2} + 2 \times y)
( = 12{x^3} + 3xy + 8{x^2} + 2y)
( = 12{x^3} + 8{x^2} + 3xy + 2y)

#### Division of algebraic expressions

Splitting algebraic identities can be done in two ways:

(i) Use of algebraic identity

We can use any standard algebraic identity for division as shown below:

(frac{{{x^3} – 8}}{{x – 2}} = frac{{{{(x)}^3} – {{(2)}^3}}}{{x – 2 }} = \frac{{(x – 2) left[ {{{(x)}^2} + x mal 2 + {{(2)}^2}} \right]}}{{x – 2} }\)
( = {x^2} + 2x + 4)

(Video) Algebraic Expressions – Algebra Basics

Here the algebraic identity ({a^3} - {b^3} = (a - b)({a^2} + ab + {b^2})) is used.

(ii) Using the long division method

In cases where algebraic identities cannot be used, the long division method is used in the same way we use it for dividing large numbers.

In this division, the dividend is ({x^2} + 3x + 1) , the divisor is (x – 1), the quotient is (x + 2), and the remainder is (3)

### Formula for algebraic expressions

The formulas for algebraic expressions are the standard algebraic identities used to solve problems related to the algebraic expressions. We give some of the formulas below (the list is not exhaustive):

1. ({a^2} – {b^2} = (a – b)(a = b))
2. ({(a + b)^2} = {a^2} + 2ab + {b^2})
3. ({(a – b)^2} = {a^2} – 2ab + {b^2})
4. ({(a + b + c)^3} = {a^2} + {b^2} + {c^2} = 2ab + 2bc + 2ca)
5. ({(a + b)^3} = {a^3} + 3{a^2}b + 3a{b^2} + {b^3} = {a^3} + {b^3 } + 3ab(a + b))
6. ({(a – b)^3} = {a^3} – 3{a^2}b + 3a{b^2} – {b^3} = {a^3} – {b^3 } – 3ab(a-b))
7. ({a^3} – {b^3} = (a-b)({a^2} + ab + {b^2}))
8. ({a^3} – {b^3} = (a-b)({a^2} + ab + {b^2}))
9. ({a^3} + {b^3} = (a + b)({a^2} – ab + {b^2}))
10. ({a^3} + {b^3} + {c^3} – 3abc = (a + b + c)({a^2} + {b^2} + {c^2} – ab – bc – ca))

### Solved examples of algebraic expressions

Students can review the solved algebraic expression examples below to prepare for various exams:

Q1. Addiere (5{x^2} – 7x + 3,) ( – 8{x^2} + 2x – 5) und (7{x^2} – x – 2)
A1
. The solution is given below:
= (5{x^2} – 7x + 3) + ( – 8{x^2} + 2x – 5) + (7{x^2} – x – 2))
= 5{x^2} - 8{x^2} + 7{x^2} - 7x + 2x - x + 3 - 5 - 2) (collect similar terms)
= (5 – 8 + 7){x^2} + ( – 7 + 2 – 1)x + (3 – 5 – 2)) (add like terms)
= 4{x^2} – 6x – 4).

Q2. Subtract ((2{x^2} - 5x + 7) from ((3{x^2} + 4x - 6))
A2
. ((3{x^2} + 4x – 6) – (2{x^2} – 5x + 7))
= 3{x^2} + 4x – 6 – 2{x^2} + 5x – 7)
= {x^2} + 9x – 13).

Q3 Multiply: $$– 8a{b^2}c,3{a^2}b$$ and $$– \frac{1}{6}$$
A3.
(left( { – 8 times 3 times frac{{ – 1}}{6}} right) times (3{a^2}b) times left( { – frac{1}{6}} right) ) ( left ( { – 8 times 3 times frac{{ – 1}}{6}} right) times (a times {a^2} times {b^2} times b times c) ) ( = 4{a^{(1 + 2)}} times {b^{(2 + 1)}} times c = 4{a^3}{b^3}c ).

Q4 Simplify the expression: $$12{m^2} - 9m + 5m - 4{m^2} - 7m + 10$$.
A4.
Rearranging the terms, we have:
= (12 – 4){m^2} + (5 – 9 – 7)m + 10)
= 8{m^2} + (-4 -, -7)m + 10)
= 8{m^2} + ( – 11)m + 10)
= 8{m^2} – 11m + 10).

Q5. What is the degree of the monomial (7)?
A5.
We know that the degree of every constant term is zero ((0)). Hence the degree of the monomial (7) is (0).

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### FAQs on algebraic expressions

F.1: What is an algebraic expression and equation?
Answer: The algebraic expression is a combination of numbers and variables and operation symbols. An equation consists of two expressions joined by an equals sign.

F.2: What are basic algebraic expressions?
Answer: The combination of the constants and the variables connected by the signs of the basic operations of addition, subtraction, multiplication and division is called an algebraic expression.

(Video) Algebraic Expressions (Basics)

Q.3: What types of algebraic expressions are there?
Answer: In terms of the number of terms present, the algebraic expressions are classified as monomial, binomial, trinomial, quadrinomial, polynomial, etc.
In terms of the number of variables present, the algebraic expressions are classified as one-variable, two-variable, three-variable, and so on.

Q.4: What is an algebra formula?
Answer: The various formulas used to solve problems related to algebraic expressions are called the algebraic formula. Some of them are:
({a^2} – {b^2} = (a – b)(a + b))
({(a + b)^2} = {a^2} + 2ab + {b^2})
({(a – b)^2} = {a^2} – 2ab + {b^2})
({(a + b + c)^3} = {a^2} + {b^2} + {c^2} = 2ab + 2bc + 2ca)
({(a + b)^3} = {a^3} + 3{a^2}b + 3a{b^2} + {b^3} = {a^3} + {b^3} + 3ab(a+b))
({(a – b)^3} = {a^3} – 3{a^2}b + 3a{b^2} – {b^3} = {a^3} – {b^3} – 3ab(a – b))
({a^3} – {b^3} = (a-b)({a^2} + ab + {b^2}))
({a^3} + {b^3} = (a + b)({a^2} – ab + {b^2}))
({a^3} + {b^3} + {c^3} – 3abc = (a + b + c)({a^2} + {b^2} + {c^2} – ab – bc – ca))

F.5: Is 5 an algebraic expression?
Answer:Yes, 5 is an algebraic expression. It is a monomial with only one constant term (5).

## FAQs

### Algebraic expressions: definition, formulas, example? ›

In mathematics, an algebraic expression is an expression built up from constant algebraic numbers, variables, and the algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number). For example, 3x2 − 2xy + c is an algebraic expression.

What is an example of algebraic expression formula? ›

For example, 2 × (x + 8y) is an algebraic expression. An algebraic expression is an expression that consists of constants, variables, and some algebraic operations. For example, 3x^2 − 2xy + d is an algebraic expression.

What are the 10 algebraic formulas? ›

10th Algebra Formulas
• (a + b)2 = a2 + 2ab + b2.
• (a − b)2 = a2 − 2ab + b2.
• (a + b)(a – b) = a2 – b2.
• (x + a)(x + b) = x2 + (a + b)x + ab.
• (x + a)(x – b) = x2 + (a – b)x – ab.
• (x – a)(x + b) = x2 + (b – a)x – ab.
• (x – a)(x – b) = x2 – (a + b)x + ab.
• (a + b)3 = a3 + b3 + 3ab(a + b)

What are 2 examples of algebraic expression? ›

An algebraic expression is a mathematical phrase where variables and constants are combined using the operational (+, -, × & ÷) symbols. An algebraic symbol lacks the equal (=) sign. For example, 10x + 63 and 5x – 3 are examples of algebraic expressions.

What are 4 algebraic expressions? ›

Types of Algebraic Expressions | Monomial | Polynomial | Binomial | Trinomial.

What are the most common formulas? ›

Elementary & Middle School
• Slope Formula: Slope = y₂ – y₁ / x₂ – x₁ ...
• Slope Intercept Formula: y=mx+b. ...
• Area of Triangle: Area = (1/2) (base) (height) ...
• Sine (SOH): Sine = opposite / hypotenuse. ...
• Cosine (CAH): Cosine = adjacent / hypotenuse. ...
• Tangent (TOA): Tangent = opposite / adjacent. ...
• The Pythagorean Theorem: a²+b²=c²
Jun 21, 2022

What are 2 terms in algebraic expression? ›

A term can be a number, a variable, product of two or more variables or product of a number and a variable. An algebraic expression is formed by a single term or by a group of terms. For example, in the expression 4x + y, the two terms are 4x and y.

What are the 12 algebraic identities? ›

List of Standard Identities
• (a + b)2 = a2 + b2 + 2ab.
• (a – b)2 = a2 + b2 – 2ab.
• (a + b)3 = a3 + b3 + 3ab(a + b) = a3 + b3 + 3a2b + 3ab. ...
• (a – b)3 = a3 – b3 – 3ab(a – b) = a3 – b3 – 3a2b + 3ab. ...
• (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca.
• a3 – b3 = (a – b)(a2 + ab + b2)
• a3 + b3 = (a + b)(a2 – ab + b2)

What are all the algebra 1 formulas? ›

• x2 – x1. Linear Equations. Slope-intercept Form: y = mx + b. Point-slope Form: y – y1 = m(x – x1) Standard Form: Ax + By = C. ...
• • r n – 1.
• Compound Interest Formula. A = P(1 + r } n )
• nt.
• Quadratic Formulas. Quadratic Equations. Standard Form: y = ax2 + bx + c. Vertex Form: y = a(x – h)2 + k. ...
• −b ± √
• _______
• b2 – 4ac.

What are basic algebraic expressions? ›

What are Algebraic Expressions? An algebraic expression (or) a variable expression is a combination of terms by the operations such as addition, subtraction, multiplication, division, etc. For example, let us have a look at the expression 5x + 7. Thus, we can say that 5x + 7 is an example of an algebraic expression.

### What is a formula in algebra? ›

A formula is a mathematical rule or relationship that uses letters to represent amounts which can be changed – these are called variables. For example, the formula to work out the area of a triangle. Triangle area = b h 2 (where represents the base of the triangle and represents the height of the triangle).

What is a algebraic expression for kids? ›

An algebraic expression is an expression involving variables and constants, along with algebraic operations: addition, subtraction, multiplication, and division. An example of an algebraic expression is: 3x + 1 and 5(x² + 3x)

What is the popular algebra formula? ›

Here are some of the most commonly used formulas of algebra: a2 - b2 = (a - b)(a + b) (a + b)2 = a2 + 2ab + b. (a - b)2 = a2 - 2ab + b.

What is the best math formula? ›

Euler's identity is considered to be "the finest of equations" in maths classes because it describes an unlikely combination of five mathematical constants. Euler's equation (published by Leonhard Euler in 1755) applies in the case of a perfect fluid.

How many types of algebra formulas are there? ›

Types of Algebraic Equations

A few of the equations in algebra are: Polynomial Equations. Quadratic Equations. Cubic Equations.

What are the types of algebraic expression? ›

TYPES OF ALGEBRAIC EXPRESSIONS
• BINOMIALS: An algebraic expression containing 2 terms is called a binomial. ...
• TRINOMIALS: An algebraic expression containing 3 terms is called a trinomial. ...
• MULTINOMIAL: ...
• POLYNOMIALS: ...
• DEGREE OF A POLYNOMIAL IN ONE VARIABLE: ...
• LINEAR POLYNOMIAL: ...
• CUBIC POLYNOMIAL:

What is an example of an expression and an equation? ›

We can say that an expression is a random combination of numbers, variables, functions, etc. For example, 3x - 2 is an expression. While on the other hand, an equation means that two different expressions are connected to each other by an equal to sign in between, For example, 3x - 2 = 5 + x is an equation.

How do you write an expression in math? ›

How do you Write an Expression in Math? We write an expression in math by using numbers or variables and mathematical operators which are addition, subtraction, multiplication, and division. For example, the expression of the mathematical statement "4 added to 2", will be 2+4.

What is the number pattern formula? ›

The formula for the nth term of a linear number pattern, denoted an, is an = dn - c, where d is the common difference in the linear pattern and c is a constant number.

How do you solve algebraic word problems easily? ›

You can tackle any word problem by following these five steps:
1. Read through the problem carefully, and figure out what it's about.
2. Represent unknown numbers with variables.
3. Translate the rest of the problem into a mathematical expression.
4. Solve the problem.

### How do you start an algebraic expression? ›

Any algebraic expression is created with a combination of variables and numbers using the arithmetic operations like subtraction, addition, division, multiplication, and exponentiation. The term can either be a variable, a number or a product of a variable and number with an exponent.

What is simple formulas? ›

Simple formulas always start with an equal sign (=), followed by constants that are numeric values and calculation operators such as plus (+), minus (-), asterisk(*), or forward slash (/) signs. Let's take an example of a simple formula. On the worksheet, click the cell in which you want to enter the formula.

What are three formulas? ›

The following are the three equations of motion:
• First Equation of Motion : v = u + a t.
• Second Equation of Motion : s = u t + 1 2 a t 2.
• Third Equation of Motion : v 2 = u 2 + 2 a s.

How can I learn all formulas? ›

Practice, practice and practice: Practice makes you perfect! When you practice using the formulas you want to learn, your brain understands the application of the formula and remembers it. Try solving and practicing problems using the formula and you will see results! Repetition leads to memorization.

What is a B in algebra? ›

A and B in algebra stand for any variables of real numbers. A real number is a value of a continuous quantity that can represent a distance along a line.

What is algebra class 8? ›

Algebra is one of the major parts of Mathematics in which general symbols and letters are used to represent quantities and numbers in equations and formulae. The more basic parts of algebra are called elementary algebra and more abstract parts are called modern algebra or abstract algebra.

What are the first 4 identities in algebra? ›

The standard algebraic identities are:

(a + b)2 = a2 + 2ab + b. (a – b)2 = a2 – 2ab + b. a2 – b2 = (a + b)(a – b) (x + a)(x + b) = x2 + (a + b) x + ab.

Is algebra 1 or 2 harder? ›

Because Algebra 2 builds on and combines material from past math classes as well as includes additional miscellaneous concepts, it is inherently a level above Algebra 1 in terms of difficulty; however, if the student did not struggle with Algebra 1, the addition of new material introduced in Algebra 2 should not be too ...

What are all the algebraic rules? ›

There are five fundamental rules that makeup algebra. They are as follows: Commutative Rule of Addition, Commutative Rule of Multiplication, Associative Rule of Addition, Associative Rule of Multiplication, Distributive Rule of Multiplication.

What is the hardest algebra formula? ›

For decades, a math puzzle has stumped the smartest mathematicians in the world. x3+y3+z3=k, with k being all the numbers from one to 100, is a Diophantine equation that's sometimes known as "summing of three cubes."

### What is the most famous algebra formula? ›

Kane and Morton M. Sternheim,' says: The equation E = Mc2 is perhaps the most famous equation of twentieth- century physics. It is a statement that mass and energy are two forms of the same thing, and that one can be converted into the other (ibid., p.

What is the most famous algebraic equation? ›

When it was first discovered, it was groundbreaking. Einstein's E=mc² is the world's most famous equation. Simple as that. It is short, it is elegant, and it describes a phenomenon so crucial that everyone should know about it.

What are the 4 identities with examples? ›

The Four Basic Identities in Maths Class 8 have Been Listed Below
Identity I(a+b)2 = a2+2ab+b2
Identity II(a-b)2 = a2- 2ab+b2
Identity IIIa2-b2= (a+b) (a-b)
Identity IV(x+a) (x+b) = x2+(a+b) x+ab

What are the basic rules of algebra? ›

What are the four basic rules of algebra? The basic rules of algebra are the commutative rule of addition, the commutative rule of multiplication, the associative rule of addition, the associative rule of multiplication, and the distributive property of multiplication.

What's the hardest algebra? ›

For decades, a math puzzle has stumped the smartest mathematicians in the world. x3+y3+z3=k, with k being all the numbers from one to 100, is a Diophantine equation that's sometimes known as "summing of three cubes."

What is the hardest math equation? ›

The equation x3+y3+z3=k is known as the sum of cubes problem. While seemingly straightforward, the equation becomes exponentially difficult to solve when framed as a “Diophantine equation” — a problem that stipulates that, for any value of k, the values for x, y, and z must each be whole numbers.

What is the golden rule of algebra in math? ›

Golden Rule of Algebra: “Do unto one side of the equal sign as you will do to the other…” **Whatever you do on one side of the equal sign, you MUST do the same exact thing on the other side. If you multiply by -2 on the left side, you have to multiply by -2 on the other.

How many algebras are there? ›

Algebra is divided into different sub-branches such as elementary algebra, advanced algebra, abstract algebra, linear algebra, and commutative algebra.

What is the longest math formula? ›

What is the world's longest equation? Answer – The Boolean Pythagorean Triples issue was initially introduced in the 1980s by California-based mathematician Ronald Graham is the longest arithmetic equation, according to Sciencealert, and includes roughly 200 gigabytes of text.

What is the number 1 in algebra? ›

Definitions. Mathematically, 1 is: in arithmetic (algebra) and calculus, the natural number that follows 0 and the multiplicative identity element of the integers, real numbers and complex numbers; more generally, in algebra, the multiplicative identity (also called unity), usually of a group or a ring.

### Who is the 12 father of algebra? ›

Muhammad ibn Musa al-Khwarizmi was a 9th-century Muslim mathematician and astronomer. He is known as the “father of algebra”, a word derived from the title of his book, Kitab al-Jabr.

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