Factor by Grouping -x^3+y^3

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

Step 1

Rewrite $- x^{3}$ as ${(- x)}^{3}$ .

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

Step 2

Since both terms are perfect cubes, factor using the sum of cubes formula, $a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})$ where $a = - x$ and $b = y$ .

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

Step 3

Simplify.

Apply the product rule to $- x$ .

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

Raise $- 1$ to the power of $2$ .

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

Multiply $x^{2}$ by $1$ .

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

Multiply $- - x$ .

Multiply $- 1$ by $- 1$ .

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

Multiply $x$ by $1$ .

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

Factor by Grouping -x^3+y^3

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