Solve x[2y-(-x^2+xy-3)y-x^2y+x(y^2-x)]+x^3

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

Evaluate

$$5xy$$

Solution Steps

Use the distributive property to multiply -x^{2}+xy-3 by y.

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

To find the opposite of \left(-x^{2}\right)y+xy^{2}-3y, find the opposite of each term.

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

Multiply -1 and -1 to get 1.

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

Combine 2y and 3y to get 5y.

$$x\left(5y+x^{2}y-xy^{2}-x^{2}y+x\left(y^{2}-x\right)\right)+x^{3}$$

Combine x^{2}y and -x^{2}y to get 0.

$$x\left(5y-xy^{2}+x\left(y^{2}-x\right)\right)+x^{3}$$

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

$$x\left(5y-xy^{2}+xy^{2}-x^{2}\right)+x^{3}$$

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

$$x\left(5y-x^{2}\right)+x^{3}$$

Use the distributive property to multiply x by 5y-x^{2}.

$$5xy-x^{3}+x^{3}$$

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

$$5xy$$

Expand

$$5xy$$

Solution Steps

Use the distributive property to multiply -x^{2}+xy-3 by y.

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

To find the opposite of \left(-x^{2}\right)y+xy^{2}-3y, find the opposite of each term.

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

Multiply -1 and -1 to get 1.

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

Combine 2y and 3y to get 5y.

$$x\left(5y+x^{2}y-xy^{2}-x^{2}y+x\left(y^{2}-x\right)\right)+x^{3}$$

Combine x^{2}y and -x^{2}y to get 0.

$$x\left(5y-xy^{2}+x\left(y^{2}-x\right)\right)+x^{3}$$

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

$$x\left(5y-xy^{2}+xy^{2}-x^{2}\right)+x^{3}$$

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

$$x\left(5y-x^{2}\right)+x^{3}$$

Use the distributive property to multiply x by 5y-x^{2}.

$$5xy-x^{3}+x^{3}$$

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

$$5xy$$