Difference of Squares Formula

About Difference of Squares Formula

This is one of the most used algebraic formulas for expanding a term of the form a2 - b2. In other words, it's an algebraic form of an equation for equating the discrepancies between two square numbers. This formula can be used to simplify a complicated equation. You can get all Maths formulas on one-page visit the Maths Formulas section of HT. 

Difference of Squares Calculation Formula

The difference of squares formula is as follows:

a2 − b2 = (a − b)(a + b) or a2 − b2 = (a + b) (a − b)

Proof:

An equation taken: 132 – 82

According to the difference of squares formula,

a2 − b2 = (a + b) (a − b)

Here, a = 13; b = 8;

LHS = a2 − b2

= 132 − 82

= 169 – 64

= 105

RHS = (a + b)(a − b)

= (13 + 8)(13 – 8) = 21 × 5 = 105

Thus, LHS = RHS

Solved example of Difference of Squares Formula

Example: What is the value of 102 − 42?

Sol: The formula for difference of squares is, a2 − b2 = (a + b)(a − b)

From the given expression, we have

a = 10 ; b = 4;

a2 − b2 = 102 − 42

= (10 + 4) (10 − 4)

= 14 × 6

= 84

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Difference of Squares Formula

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