Question

Provide an example of a difference of perfect squares and show how to factor it completely.

Answer 1

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When an expression can be viewed as the difference of two perfect squares, i.e. a²-b², then we can factor it as (a+b)(a-b). For example, x²-25 can be factored as (x+5)(x-5). This method is based on the pattern (a+b)(a-b)=a²-b², which can be verified by expanding the parentheses in (a+b)(a-b).

Answer 2

$100 {}^{2} - 99 {}^{2} = (100 - 99)(100 + 99)$

$100 {}^{2} - 99 {}^{2} = 199$

We can establish the relation:

$x {}^{2} - y {}^{2} = (x - y)(x + y)$

or vice versa.

$(x - 2)(x + 2) = x {}^{2} - 4$

$4x {}^{2} - 49 = (2x - 7)(2x + 7)$