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How do you factor $- 12 x^{2} + 27$ $-12x^2+27$ ?

1 Answer

Mar 17, 2017

$- 3 (2 x - 3) (2 x + 3)$ $-3(2x-3)(2x+3)$

Explanation:

Given
$XXX - 12 x^{2} + 27$ $color(white)("XXX")-12x^2+27$

we can remove the obvious integer factor $(- 3)$ $(-3)$ to get
$XXX (- 3) (4 x^{2} - 9)$ $color(white)("XXX")(-3)(4x^2-9)$

then recognizing $(4 x^{2} - 9)$ $(4x^2-9)$ as the difference of squares: $({(2 x)}^{2} - {(3)}^{2})$ $((2x)^2-(3)^2)$
with factors $(2 x - 3)$ $(2x-3)$ and $(2 x + 3)$ $(2x+3)$

we obtain the result given above.

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