Solve x(x^2-1)+x^2(x+2)-x(5-x^2)

$$x ( x ^ { 2 } - 1 ) + x ^ { 2 } ( x + 2 ) - x ( 5 - x ^ { 2 } )$$

Evaluate

$$x\left(3x^{2}+2x-6\right)$$

Solution Steps

Use the distributive property to multiply x by x^{2}-1.

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

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

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

Combine x^{3} and x^{3} to get 2x^{3}.

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

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

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

To find the opposite of 5x-x^{3}, find the opposite of each term.

$$2x^{3}-x+2x^{2}-5x+x^{3}$$

Combine -x and -5x to get -6x.

$$2x^{3}-6x+2x^{2}+x^{3}$$

Combine 2x^{3} and x^{3} to get 3x^{3}.

$$3x^{3}-6x+2x^{2}$$

Expand

$$3x^{3}+2x^{2}-6x$$

Solution Steps

Use the distributive property to multiply x by x^{2}-1.

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

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

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

Combine x^{3} and x^{3} to get 2x^{3}.

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

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

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

To find the opposite of 5x-x^{3}, find the opposite of each term.

$$2x^{3}-x+2x^{2}-5x+x^{3}$$

Combine -x and -5x to get -6x.

$$2x^{3}-6x+2x^{2}+x^{3}$$

Combine 2x^{3} and x^{3} to get 3x^{3}.

$$3x^{3}-6x+2x^{2}$$