Algebraic Expressions Formula

Algebraic Expressions Formula – Algebraic expressions are the concept of expressing numbers with letters or alphabets without stating their real values. The fundamentals of algebra taught us how to express an unknown value with letters such as x, y, and z. These letters are referred to as variables. An algebraic expression can consist of both variables and constants. A coefficient is defined as any value that comes before and is multiplied by another variable.

Algebraic Expressions Formula

In mathematics, an algebraic expression is one that combines variables and constants as well as algebraic operations (addition, subtraction, and so on). Expressions are composed of terms. Solve questions in Algebraic Expressions Worksheets at Extramark’s.

Examples –

6x + 2y – 4,  3x – 8, etc.

These expressions are represented using unknown variables, constants, and coefficients. The combination of these three terms is referred to as an expression. Algebraic expressions, unlike algebraic equations, do not have sides or equal sign.

Example: 3x + 5

  • x is a variable, whose value is unknown to us which can take any value.
  • 3 is known as the coefficient of x, as it is a constant value used with the variable term and is well defined.
  • 5 is the constant value term that has a definite value.

The whole expression is known to be the Binomial term, as it has two unlikely terms.

Algebraic Expression Types

There are 3 main types of algebraic expressions which include:

  • Monomial Expression – An algebraic expression which is having only one term is known as a monomial. Examples – 3x4, 3xy, 3x, 8y, etc.
  • Binomial Expression – A binomial expression is an algebraic expression which is having two terms, which are unlike. Examples – 5xy + 8, xyz + x3, etc.
  • Polynomial Expression – In general, an expression with more than one term with non-negative integral exponents of a variable is known as a polynomial. Examples – ax by ca,  x3 + 2x + 3, etc.

List of Algebraic Expression Formula

  • a² – b² = (a-b)(a+b)
  • (a+b)² = a² + 2ab + b²
  • (a-b)² = a² – 2ab + b²
  • a² + b² = (a-b)² +2ab
  • (a+b+c)² = a²+b²+c²+2ab+2ac+2bc
  • (a-b-c)² = a²+b²+c²-2ab-2ac+2bc
  • a³-b³ = (a-b) (a² + ab + b²)
  • a³+b³ = (a+b) (a² – ab + b²)
  • (a+b)³ = a³+ 3a²b + 3ab² + b³
  • (a-b)³ = a³- 3a²b + 3ab² – b³
  • (a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4
  • (a – b)4 = a4 – 4a3b + 6a2b2 – 4ab3 + b4
  • a4 – b4 = (a – b)(a + b)(a2 + b2)
  • a5 – b5 = (a – b)(a4 + a3b + a2b2 + ab3 + b4)
  • “n” is a natural number, an – bn = (a-b) (an-1 + an-2b +….bn-2a + bn-1)
  • “n” is a even number, an + bn = (a+b) (an-1 – an-2b +….+ bn-2a – bn-1)
  • “n” is an odd number an + bn = (a-b) (an-1 – an-2b +…. – bn-2a + bn-1)
  • (am)(an) = am+n (ab)m = amn

Algebraic Expressions Solved Examples

Example: Simplify the given expressions by combining the like terms and write the type of Algebraic expression.

(i) 5xy­­3 + 4x2 y3 + 3y3x

(ii) 5ab2 c2 + 2a3 b2 − 3abc – 5ab2 c2 – 2b2 a3 + 2ab

(iii) 50x3 – 20x + 8x + 21x3 – 3x + 15x – 41x3


Creating a table to find the solution:

S.No Term Simplification Type of Expression
1 5xy­­3 + 4x2 y3 + 3y3x 8xy3 + 4x2y3 Binomial
2 7ab2 c2 + 4a3 b2 – 3ab2 c2 – 2b2 a3 4ab2 c2 + 2b2 a3
3 30x3 – 20x + 8x + 21x3 – 3x + 15x – 41x3 10x³ Monomial

Example 2: Find the value of 10² – 6²

Solution: Now these are simple numbers, so we can calculate the answer. But the correct method is to apply the formula,

a² – b² = (a-b)(a+b)

10² – 6² = (10-6)(10+6) = 4 × 16 = 64

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FAQs (Frequently Asked Questions)

1. Is 6 an algebraic expression?

No, 6 is not an algebraic expression because an expression should have at least one variable and one operation to be algebraic.

2. What is a variable in an algebraic expression?

A variable is an unknown quantity that must be determined by solving an algebraic equation.

3. What are Algebra Expressions?

For each algebra formula, the equations containing variables, powers, and arithmetic operations on each side of the equals sign are referred to as algebraic expressions/variable expressions. The terms on each side of the equals sign in the algebraic formula (a+b)(a-b)=a2 – b2 are referred to as algebraic expressions.