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.
122 – 82
As per the Difference of Squares Formula
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 $\times$ 4
= 80

Hence, LHS = RHS

Solved Examples

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


Practise This Question

Nucleus of mass number A, originally at rest, emits an α -particle with speed v. The daughter nucleus recoils with a speed