# Difference of Squares Formula

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.

The Difference of Squares Formula is given as,

\[\LARGE a^{2}-b^{2}=(a+b)(a-b)\;or\;(a-b)(a+b)\]

Let’s go through an example to proof this Difference of Squares Formula with the following problem.

12^{2} – 8^{2}

As per the Difference of Squares Formula

a^{2} – b^{2} = (a + b)(a – b)

where a = 12; b = 8

LHS

= a^{2} – b^{2}

= 12^{2} – 8^{2}

= 144 – 64

= 80

RHS

= (a + b)(a – b)

= (12 + 8)(12 – 8)

= 20 $\times$ 4

= 80

Hence, LHS = RHS

### Solved Examples

**Question: **What is the value of 10^{2} – 4^{2}?

**Solution:
**The formula for difference of squares is,

a

^{2}– b

^{2}= (a + b)(a – b)

From the given equation,

a = 10 ; b = 4

= 10

^{2}– 4

^{2}

= (10 + 4) (10 – 4)

= 14 × 6

= 84