Question #47c74

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Answer 1 · 2018-01-25T08:34:35

$3(x+1)(x-1)$

Factor out a 3 from each term in the equation:

$=3(x^2)-3(1)$

"Pull" (reverse-distribute) the 3:

$=3(x^2-1)$

$x^2-1$ = $(x+1)(x-1)$ because it's a difference of squares:

$=3(x+1)(x-1)$

Here's how differences of squares work:

$(x+1)(x-1)$
$=(x(x-1))+1(x-1)$
$=x^2-1x+1x-1$
$=x^2-1$

This is true for any variable x and a $(x+a)(x-a)$
$(x+a)(x-a)$
$=(x(x-a))+a(x-a)$
$=x^2-ax+ax-a^2$
$=x^2-a^2$