Factoring Difference of Squares

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In some cases recognizing some common patterns in the trinomial or binomial will help you to factor it faster. For example, we could check whether the binomial is a difference of squares.

How to factor Difference of Squares?

A difference of squares is a binomial of the form:

a² – b²

Take note that the first term and the last term are both perfect squares.

When we factor a difference of two squares, we will get

a² – b² = (a + b)(a – b)

This is because (a + b)(a – b) = a²– ab + ab – b² = a²– b²

Example:	x2 – 25 = 0
	x2 – 52 = 0
	(x + 5)(x – 5) = 0
	We get two values for x:

Be careful! This method only works for difference of two squares and not for the sum of two squares:
a² + b² ≠ (a + b)(a – b)

Example :

Factor
a) x²– 9
b) 4x²– 25
c) 2x²– 32
d) πR²– πr²

Solution:

a) x²– 9
= x²– 3²
= (x + 3)(x – 3)

b) 4x²– 25
= (2x)²– (5)²
= (2x + 5)(2x – 5)

c) 2x²– 32
= 2(x²– 16)
= 2(x² – 4²)
= 2(x + 4)(x – 4)

d) πR²– πr²
= π(R²– r²)
= π(R + r)(R – r)

The following videos explain how to factor a difference of squares.