Difference of squares
Every algebraic expression in the form of a2 - b2
can be factored, or decomposed, into a product of factors in the following
way;
a2 - b2 = (a + b)(a - b)
or
a2 - b2 = (a - b)(a + b)
Example 1
x2 - y2 = (x+y)(x-y)
Example 2
x2 - 9 = (x+3)(x-3)
Example 3
9m2 - 25n2 = (3m+5n)(3m-5n)
Example 4
(x+y)2-(a+b)2 = [(x+y)+(a+b)][(x+y)-(a+b)]
Example 5
a2 - 5 = a2 - 
52 = (a+5)(a-5)
Example 6
a4 - b4 = (a2+b2)(a2-b2) = (a2+b2)(a+b)(a-b)
N. B. a2+b2 does not decompose into a product of factors.
Before proceeding to the exercises, ensure that you have a pencil and some
paper handy.
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