Pre-Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Simplify.

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Step 1.2.1

Multiply $- 2$ by $- 1$ .

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

Step 1.2.2

Multiply $2$ by $- 1$ .

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

Step 1.2.3

Multiply $- - y^{3}$ .

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Step 1.2.3.1

Multiply $- 1$ by $- 1$ .

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

Step 1.2.3.2

Multiply $y^{3}$ by $1$ .

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

Step 1.3

Remove parentheses.

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

Step 2

Simplify by adding terms.

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Step 2.1

Combine the opposite terms in $2 x y^{2} + 2 x^{3} - x^{2} y + 2 x^{2} y - 2 x y^{2} + y^{3}$ .

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Step 2.1.1

Subtract $2 x y^{2}$ from $2 x y^{2}$ .

$2 x^{3} - x^{2} y + 2 x^{2} y + 0 + y^{3}$

Step 2.1.2

Add $2 x^{3} - x^{2} y + 2 x^{2} y$ and $0$ .

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

Step 2.2

Add $- x^{2} y$ and $2 x^{2} y$ .

$2 x^{3} + 1 x^{2} y + y^{3}$

Step 2.3

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

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