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 formula for the difference of squares is given as,
| a2 − b2 = (a + b) (a − b)
or, a2 − b2 = (a − b) (a + b) |
Also Check: Sum of Squares Formula
Let’s go through an example given below to prove this difference of squares formula.
Proof:
Take an equation: 122 – 82
As per the formula for difference of squares,
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: What is the value of 102 − 42?
Solution:
The formula for difference of squares is,
a2 − b2 = (a + b)(a − b)
From the given expression,
a = 10 ;
b = 4;
a2 − b2 = 102 − 42
= (10 + 4) (10 − 4)
= 14 × 6
= 84
Very helpful for many kinds of exams and they have divided the subjects into various parts to make students more convenient to understand.