Solve xy(y+y^2)-y^2(xy-x)+2x(x-y^2)

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

Evaluate

$$2x^{2}$$

Solution Steps

Use the distributive property to multiply xy by y+y^{2}.

$$xy^{2}+xy^{3}-y^{2}\left(xy-x\right)+2x\left(x-y^{2}\right)$$

Use the distributive property to multiply y^{2} by xy-x.

$$xy^{2}+xy^{3}-\left(xy^{3}-y^{2}x\right)+2x\left(x-y^{2}\right)$$

To find the opposite of xy^{3}-y^{2}x, find the opposite of each term.

$$xy^{2}+xy^{3}-xy^{3}+y^{2}x+2x\left(x-y^{2}\right)$$

Combine xy^{3} and -xy^{3} to get 0.

$$xy^{2}+y^{2}x+2x\left(x-y^{2}\right)$$

Combine xy^{2} and y^{2}x to get 2xy^{2}.

$$2xy^{2}+2x\left(x-y^{2}\right)$$

Use the distributive property to multiply 2x by x-y^{2}.

$$2xy^{2}+2x^{2}-2xy^{2}$$

Combine 2xy^{2} and -2xy^{2} to get 0.

$$2x^{2}$$

Expand

$$2x^{2}$$

Solution Steps

Use the distributive property to multiply xy by y+y^{2}.

$$xy^{2}+xy^{3}-y^{2}\left(xy-x\right)+2x\left(x-y^{2}\right)$$

Use the distributive property to multiply y^{2} by xy-x.

$$xy^{2}+xy^{3}-\left(xy^{3}-y^{2}x\right)+2x\left(x-y^{2}\right)$$

To find the opposite of xy^{3}-y^{2}x, find the opposite of each term.

$$xy^{2}+xy^{3}-xy^{3}+y^{2}x+2x\left(x-y^{2}\right)$$

Combine xy^{3} and -xy^{3} to get 0.

$$xy^{2}+y^{2}x+2x\left(x-y^{2}\right)$$

Combine xy^{2} and y^{2}x to get 2xy^{2}.

$$2xy^{2}+2x\left(x-y^{2}\right)$$

Use the distributive property to multiply 2x by x-y^{2}.

$$2xy^{2}+2x^{2}-2xy^{2}$$

Combine 2xy^{2} and -2xy^{2} to get 0.

$$2x^{2}$$