Factor -2y^3-2y^2+2y+2

$- 2 y^{3} - 2 y^{2} + 2 y + 2$

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

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

$2 (- y^{3}) - 2 y^{2} + 2 y + 2$

Factor $2$ out of $- 2 y^{2}$ .

$2 (- y^{3}) + 2 (- y^{2}) + 2 y + 2$

Factor $2$ out of $2 y$ .

$2 (- y^{3}) + 2 (- y^{2}) + 2 (y) + 2$

Factor $2$ out of $2$ .

$2 (- y^{3}) + 2 (- y^{2}) + 2 (y) + 2 (1)$

Factor $2$ out of $2 (- y^{3}) + 2 (- y^{2})$ .

$2 (- y^{3} - y^{2}) + 2 (y) + 2 (1)$

Factor $2$ out of $2 (- y^{3} - y^{2}) + 2 (y)$ .

$2 (- y^{3} - y^{2} + y) + 2 (1)$

Factor $2$ out of $2 (- y^{3} - y^{2} + y) + 2 (1)$ .

$2 (- y^{3} - y^{2} + y + 1)$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$2 ((- y^{3} - y^{2}) + y + 1)$

Factor out the greatest common factor (GCF) from each group.

$2 (y^{2} (- y - 1) - 1 (- y - 1))$

Factor the polynomial by factoring out the greatest common factor, $- y - 1$ .

$2 ((- y - 1) (y^{2} - 1))$

Rewrite $1$ as $1^{2}$ .

$2 ((- y - 1) (y^{2} - 1^{2}))$

Factor.

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = y$ and $b = 1$ .

$2 ((- y - 1) ((y + 1) (y - 1)))$

Remove unnecessary parentheses.

$2 ((- y - 1) (y + 1) (y - 1))$

Factor.

Combine exponents.

Factor $- 1$ out of $- y$ .

$2 ((- (y) - 1) (y + 1) (y - 1))$

Rewrite $- 1$ as $- 1 (1)$ .

$2 ((- (y) - 1 (1)) (y + 1) (y - 1))$

Factor $- 1$ out of $- (y) - 1 (1)$ .

$2 (- (y + 1) (y + 1) (y - 1))$

Rewrite $- (y + 1)$ as $- 1 (y + 1)$ .

$2 (- 1 (y + 1) (y + 1) (y - 1))$

Raise $y + 1$ to the power of $1$ .

$2 (- 1 ({(y + 1)}^{1} (y + 1)) (y - 1))$

Raise $y + 1$ to the power of $1$ .

$2 (- 1 ({(y + 1)}^{1} {(y + 1)}^{1}) (y - 1))$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2 (- 1 {(y + 1)}^{1 + 1} (y - 1))$

Add $1$ and $1$ .

$2 (- 1 {(y + 1)}^{2} (y - 1))$

Remove unnecessary parentheses.

$2 \cdot - 1 {(y + 1)}^{2} (y - 1)$

Combine exponents.

Factor out negative.

$- (2 {(y + 1)}^{2} (y - 1))$

Multiply $2$ by $- 1$ .

$- 2 ({(y + 1)}^{2} (y - 1))$

Remove unnecessary parentheses.

$- 2 {(y + 1)}^{2} (y - 1)$

Factor -2y^3-2y^2+2y+2

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