Factor -2x^3+8x^2-8x

$- 2 x^{3} + 8 x^{2} - 8 x$

Step 1

Factor $- 2 x$ out of $- 2 x^{3} + 8 x^{2} - 8 x$ .

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

$- 2 x (x^{2}) + 8 x^{2} - 8 x$

Factor $- 2 x$ out of $8 x^{2}$ .

$- 2 x (x^{2}) - 2 x (- 4 x) - 8 x$

Factor $- 2 x$ out of $- 8 x$ .

$- 2 x (x^{2}) - 2 x (- 4 x) - 2 x (4)$

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

$- 2 x (x^{2} - 4 x) - 2 x (4)$

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

$- 2 x (x^{2} - 4 x + 4)$

Step 2

Factor using the perfect square rule.

Rewrite $4$ as $2^{2}$ .

$- 2 x (x^{2} - 4 x + 2^{2})$

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

$4 x = 2 \cdot x \cdot 2$

Rewrite the polynomial.

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

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

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