Solve (3x+x^2-x^3)-(x^3+2x^2+5x)

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

Evaluate

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

Solution Steps

To find the opposite of x^{3}+2x^{2}+5x, find the opposite of each term.

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

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

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

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

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

Combine 3x and -5x to get -2x.

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

Expand

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

Solution Steps

To find the opposite of x^{3}+2x^{2}+5x, find the opposite of each term.

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

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

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

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

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

Combine 3x and -5x to get -2x.

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