Factor 50x^2-60x+18

$50 x^{2} - 60 x + 18$

Step 1

Factor $2$ out of $50 x^{2} - 60 x + 18$ .

Factor $2$ out of $50 x^{2}$ .

$2 (25 x^{2}) - 60 x + 18$

Factor $2$ out of $- 60 x$ .

$2 (25 x^{2}) + 2 (- 30 x) + 18$

Factor $2$ out of $18$ .

$2 (25 x^{2}) + 2 (- 30 x) + 2 (9)$

Factor $2$ out of $2 (25 x^{2}) + 2 (- 30 x)$ .

$2 (25 x^{2} - 30 x) + 2 (9)$

Factor $2$ out of $2 (25 x^{2} - 30 x) + 2 (9)$ .

$2 (25 x^{2} - 30 x + 9)$

Step 2

Factor using the perfect square rule.

Rewrite $25 x^{2}$ as ${(5 x)}^{2}$ .

$2 ({(5 x)}^{2} - 30 x + 9)$

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

$2 ({(5 x)}^{2} - 30 x + 3^{2})$

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

$30 x = 2 \cdot (5 x) \cdot 3$

Rewrite the polynomial.

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

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = 5 x$ and $b = 3$ .

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