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 Difference of Squares Formula is given as,

a2 – b2 = (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: 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 × 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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