How do you factor $(b - 3)^2 - (a + 1)^2$ ?

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Answer 1 · 2015-06-22T23:18:54

This is a difference of squares, so it factors as

$(b-3)^2 - (a+1)^2$

$= ((b-3)-(a+1))((b-3)+(a+1))$

$=(b-a-4)(b+a-2)$

For any $p$ and $q$ , we have:

$p^2-q^2 = (p-q)(p+q)$

Putting $p=(b-3)$ and $q=(a+1)$ , we have:

$(b-3)^2-(a+1)^2$

$= p^2-q^2$

$= (p-q)(p+q)$

$= ((b-3)-(a+1))((b-3)+(a+1))$

$=(b-a-4)(b+a-2)$

How do you factor (b - 3)^2 - (a + 1)^2 (b - 3)^2 - (a + 1)^2 ?