Factor 2x^3-2x^2y-84xy^2

$2 x^{3} - 2 x^{2} y - 84 x y^{2}$

Step 1

Factor $2 x$ out of $2 x^{3} - 2 x^{2} y - 84 x y^{2}$ .

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

$2 x (x^{2}) - 2 x^{2} y - 84 x y^{2}$

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

$2 x (x^{2}) + 2 x (- x y) - 84 x y^{2}$

Factor $2 x$ out of $- 84 x y^{2}$ .

$2 x (x^{2}) + 2 x (- x y) + 2 x (- 42 y^{2})$

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

$2 x (x^{2} - x y) + 2 x (- 42 y^{2})$

Factor $2 x$ out of $2 x (x^{2} - x y) + 2 x (- 42 y^{2})$ .

$2 x (x^{2} - x y - 42 y^{2})$

Step 2

Factor.

Factor by grouping.

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 1 \cdot - 42 = - 42$ and whose sum is $b = - 1$ .

Reorder terms.

$2 x (x^{2} - 42 y^{2} - x y)$

Reorder $- 42 y^{2}$ and $- x y$ .

$2 x (x^{2} - x y - 42 y^{2})$

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

$2 x (x^{2} - (x y) - 42 y^{2})$

Rewrite $- 1$ as $6$ plus $- 7$

$2 x (x^{2} + (6 - 7) (x y) - 42 y^{2})$

Apply the distributive property.

$2 x (x^{2} + 6 (x y) - 7 (x y) - 42 y^{2})$

Remove unnecessary parentheses.

$2 x (x^{2} + 6 x y - 7 (x y) - 42 y^{2})$

Remove unnecessary parentheses.

$2 x (x^{2} + 6 x y - 7 x y - 42 y^{2})$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$2 x ((x^{2} + 6 x y) - 7 x y - 42 y^{2})$

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

$2 x (x (x + 6 y) - 7 y (x + 6 y))$

Factor the polynomial by factoring out the greatest common factor, $x + 6 y$ .

$2 x ((x + 6 y) (x - 7 y))$

Remove unnecessary parentheses.

$2 x (x + 6 y) (x - 7 y)$

Factor 2x^3-2x^2y-84xy^2

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