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.
Difference of Squares
 

How to factor Difference of Squares?
A difference of squares is a binomial of the form:

a2b2

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

a2b2 = (a + b)(a – b)

This is because (a + b)(a – b) = a2ab + ab – b2 = a2b2


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)(ab)




Example:

Factor
a) x2– 9
b) 4x2– 25
c) 2x2– 32
d) πR2πr2

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) πR2πr2
= π(R2r2)
= π(R + r)(R – r)

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

Example:
Factor
x2 - 9
y2 - 1
16x2 - 25y2
x4 - 1
2x2 - 72

Example:
Factor
w2 - 81
b2 - 1/4
27a2 - 147



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