Factor 12x^2-60x+75

$12 x^{2} - 60 x + 75$

Step 1

Factor $3$ out of $12 x^{2} - 60 x + 75$ .

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

$3 (4 x^{2}) - 60 x + 75$

Factor $3$ out of $- 60 x$ .

$3 (4 x^{2}) + 3 (- 20 x) + 75$

Factor $3$ out of $75$ .

$3 (4 x^{2}) + 3 (- 20 x) + 3 (25)$

Factor $3$ out of $3 (4 x^{2}) + 3 (- 20 x)$ .

$3 (4 x^{2} - 20 x) + 3 (25)$

Factor $3$ out of $3 (4 x^{2} - 20 x) + 3 (25)$ .

$3 (4 x^{2} - 20 x + 25)$

Step 2

Factor using the perfect square rule.

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

$3 ({(2 x)}^{2} - 20 x + 25)$

Rewrite $25$ as $5^{2}$ .

$3 ({(2 x)}^{2} - 20 x + 5^{2})$

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

$20 x = 2 \cdot (2 x) \cdot 5$

Rewrite the polynomial.

$3 ({(2 x)}^{2} - 2 \cdot (2 x) \cdot 5 + 5^{2})$

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = 2 x$ and $b = 5$ .

$3 {(2 x - 5)}^{2}$