How do you factor the difference of two perfect squares: $(x+7)^2-25$ ?

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Answer 1 · 2016-11-22T22:07:26

$(x+7)^2-25 = (x+2)(x+12)$

The difference of squares identity can be written:

$a^2-b^2 = (a-b)(a+b)$

Hence we find:

$(x+7)^2-25 = (x+7)^2-5^2$

$color(white)((x+7)^2-25) = ((x+7)-5)((x+7)+5)$

$color(white)((x+7)^2-25) = (x+2)(x+12)$

How do you factor the difference of two perfect squares: (x+7)^2-25(x+7)^2-25?