Factor 12x^2-36x+27

$12 x^{2} - 36 x + 27$

Step 1

Factor $3$ out of $12 x^{2} - 36 x + 27$ .

Factor $3$ out of $12 x^{2}$ .

$3 (4 x^{2}) - 36 x + 27$

Factor $3$ out of $- 36 x$ .

$3 (4 x^{2}) + 3 (- 12 x) + 27$

Factor $3$ out of $27$ .

$3 (4 x^{2}) + 3 (- 12 x) + 3 (9)$

Factor $3$ out of $3 (4 x^{2}) + 3 (- 12 x)$ .

$3 (4 x^{2} - 12 x) + 3 (9)$

Factor $3$ out of $3 (4 x^{2} - 12 x) + 3 (9)$ .

$3 (4 x^{2} - 12 x + 9)$

Step 2

Factor using the perfect square rule.

Rewrite $4 x^{2}$ as ${(2 x)}^{2}$ .

$3 ({(2 x)}^{2} - 12 x + 9)$

Rewrite $9$ as $3^{2}$ .

$3 ({(2 x)}^{2} - 12 x + 3^{2})$

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$12 x = 2 \cdot (2 x) \cdot 3$

Rewrite the polynomial.

$3 ({(2 x)}^{2} - 2 \cdot (2 x) \cdot 3 + 3^{2})$

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = 2 x$ and $b = 3$ .

$3 {(2 x - 3)}^{2}$