Factor 3x^3+18x^2+27x

$3 x^{3} + 18 x^{2} + 27 x$

Step 1

Factor $3 x$ out of $3 x^{3} + 18 x^{2} + 27 x$ .

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

$3 x (x^{2}) + 18 x^{2} + 27 x$

Factor $3 x$ out of $18 x^{2}$ .

$3 x (x^{2}) + 3 x (6 x) + 27 x$

Factor $3 x$ out of $27 x$ .

$3 x (x^{2}) + 3 x (6 x) + 3 x (9)$

Factor $3 x$ out of $3 x (x^{2}) + 3 x (6 x)$ .

$3 x (x^{2} + 6 x) + 3 x (9)$

Factor $3 x$ out of $3 x (x^{2} + 6 x) + 3 x (9)$ .

$3 x (x^{2} + 6 x + 9)$

Step 2

Factor using the perfect square rule.

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

$3 x (x^{2} + 6 x + 3^{2})$

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

$6 x = 2 \cdot x \cdot 3$

Rewrite the polynomial.

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

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

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