Difference of Squares Formula

The difference of squares formula is one of the primary algebraic formulas which is used to expand a term which is in the form a2 âˆ’ b2. In other words, it is an algebraic form of an equation that is used to equate the differences among two square values. This formula helps to make a complex equation into a simple one.

Formula to Calculate the Difference of Squares

The formula for the difference of squares is given as,

 a2 âˆ’ b2 = (a + b) (a âˆ’ b) or, a2 âˆ’ b2 = (a âˆ’ b) (a + b)

Also Check: Sum of Squares Formula

Let’s go through an example given below to prove this difference of squares formula.

Proof:

Take an equation: 122 – 82

As per the formula for difference of squares,

a2 – b2 = (a + b)(a âˆ’ b)

where

a = 12;

b = 8;

LHS = a2 âˆ’ b2

= 122 âˆ’ 82

= 144 – 64

= 80

RHS = (a + b)(a âˆ’ b)

= (12 + 8)(12 – 8) = 20 Ã— 4 = 80

Hence, LHS = RHS

Solved Example

Question: What is the value of 102 âˆ’ 42?

Solution:

The formula for difference of squares is,

a2 âˆ’ b2 = (a + b)(a âˆ’ b)

From the given expression,

a = 10 ;

b = 4;

a2 âˆ’ b2Â = 102 âˆ’ 42

= (10 + 4) (10 âˆ’ 4)

= 14 Ã— 6

= 84