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.
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:
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: 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:
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)
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