Factor 16q^3-48q^2+36q

$16 q^{3} - 48 q^{2} + 36 q$

Step 1

Factor $4 q$ out of $16 q^{3} - 48 q^{2} + 36 q$ .

Factor $4 q$ out of $16 q^{3}$ .

$4 q (4 q^{2}) - 48 q^{2} + 36 q$

Factor $4 q$ out of $- 48 q^{2}$ .

$4 q (4 q^{2}) + 4 q (- 12 q) + 36 q$

Factor $4 q$ out of $36 q$ .

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

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

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

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

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

Step 2

Factor using the perfect square rule.

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

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

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

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

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

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

Rewrite the polynomial.

$4 q ({(2 q)}^{2} - 2 \cdot (2 q) \cdot 3 + 3^{2})$

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

$4 q {(2 q - 3)}^{2}$