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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.

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?**

Example:

*x*^{2} – 25 = 0

*x*^{2} – 5^{2} = 0

(*x* + 5)(*x* – 5) = 0

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

*x* – 5 ⇒ *x* = 5

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

More Lessons for Algebra

Math Worksheets

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.

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:

(

We get two values for

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) 4*x*^{2}– 25

c) 2*x*^{2}– 32

d) *πR*^{2}– *πr*^{2}

* Solution: *

a) *x*^{2}– 9

= *x*^{2}– 3^{2}

= (*x* + 3)(*x* – 3)

b) 4*x*^{2}– 25

= (2*x*)^{2}– (5)^{2}

= (2*x* + 5)(2*x* – 5)

c) 2*x*^{2}– 32

= 2(*x*^{2}– 16)

= 2(*x ^{2}* – 4

= 2(

d) *πR*^{2}– *πr*^{2}

= *π*(*R*^{2}– *r*^{2})

= *π*(*R + r*)(*R – r*)

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You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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