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 − 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 − b2 = (a + b) (a − b)

or,

a2 − b2 = (a − b) (a + b)

Also Check: Sum of Squares Formula

Let’s go through an example to prove this difference of squares formula with the following problem.

Proof:

Take an equation: 122 – 82

As per the formula for difference of squares,

a2 – b2 = (a + b)(a − b)

where

a = 12;

b = 8;

LHS = a2 − b2

= 122 − 82

= 144 – 64

= 80

RHS = (a + b)(a − b)

= (12 + 8)(12 – 8) = 20 × 4 = 80

Hence, LHS = RHS

Solved Example Question:

Question: What is the value of 102 − 42?

Solution:

The formula for difference of squares is,

a2 − b2 = (a + b)(a − b)

From the given equation,

a = 10 ;

b = 4;

= 102 − 42

= (10 + 4) (10 − 4)

= 14 × 6

= 84

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