The difference of squares formula is one of the primary algebraic formulas which is used to expand a term which is in the form a^{2} – b^{2}. 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 Difference of Squares Formula is given as,

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.

### Proof:

Take an equation: 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 × 4 = 80

** Hence, LHS = RHS**

### Solved Example Question:

**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