Algebra Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

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

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

Step 2

Apply the distributive property.

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

Step 3

Rewrite using the commutative property of multiplication.

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

Step 4

Rewrite using the commutative property of multiplication.

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

Step 5

Multiply $y$ by $y$ by adding the exponents.

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Step 5.1

Move $y$ .

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

Step 5.2

Multiply $y$ by $y$ .

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