How do you factor the expression $12 w^{2} - 27$ $12w^2 -27$ ?

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Answer 1 · 2015-12-13T16:56:50

$3 (2 w + 3) (2 w - 3)$ $3(2w+3)(2w-3)$

Factor out a common multiple of both terms. In this case, it's $3$ $3$ .

$3 (4 w^{2} - 9)$ $3(4w^2-9)$

Now, notice that $4 w^{2} - 9$ $4w^2-9$ is a difference of squares.

A typical difference of squares in the form $a^{2} - b^{2}$ $a^2-b^2$ can be factorized into $(a + b) (a - b)$ $(a+b)(a-b)$ .

Thus, $4 w^{2} - 9 = (2 w + 3) (2 w - 3)$ $4w^2-9=(2w+3)(2w-3)$ .

So, the complete factored form is:

$3 (2 w + 3) (2 w - 3)$ $3(2w+3)(2w-3)$

How do you factor the expression 12w^2 -2712w2−2712w^2 -27?