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.

The following diagram gives examples of factoring difference of squares. Scroll down the page for more examples and solutions.

**How to factor Difference of Squares?**

A difference of squares is a binomial of the form:

*a*^{2} – *b*^{2}

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

*a*^{2} – *b*^{2} = (*a + b*)(*a – b*)

This is because (*a + b*)(*a – b*) = *a*^{2}– *ab* + *ab – b*^{2} = *a*^{2}– *b*^{2}

Example:

x

x

(x + 5)(x – 5) = 0

We get two values for x: x + 5 ⇒ x = –5

x – 5 ⇒ x = 5

Be careful! This method only works for difference of two squares and not for the sum of two squares:

*a*^{2} + *b*^{2} ≠ (*a* + *b*)(*a* – *b*)

Example:

Factor

a) x^{2}– 9

b) 4x^{2}– 25

c) 2x^{2}– 32

d) *πR*^{2}– *πr*^{2}

Solution:

a) x^{2}– 9

= x^{2}– 3^{2}

= (x + 3)(x – 3)

b) 4x^{2}– 25

= (2x)^{2}– (5)^{2}

= (2x + 5)(2x – 5)

c) 2x^{2}– 32

= 2(x^{2}– 16)

= 2(x^{2} – 4^{2})

= 2(x + 4)(x – 4)

d) *πR*^{2}– *πr*^{2}

= *π*(*R*^{2}– *r*^{2})

= *π*(*R + r*)(*R – r*)

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

Example:

Factor

x^{2} - 9

y^{2} - 1

16x^{2} - 25y^{2}

x^{4} - 1

2x^{2} - 72

Example:

Factor

w^{2} - 81

b^{2} - 1/4

27a^{2} - 147

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