Solve x(x^2-x-1)+3(x^2+x)-1/3x(3x^2+6x)

$$x ( x ^ { 2 } - x - 1 ) + 3 ( x ^ { 2 } + x ) - \frac { 1 } { 3 } x ( 3 x ^ { 2 } + 6 x )$$

Evaluate

$$2x$$

Solution Steps

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

$$x^{3}-x^{2}-x+3\left(x^{2}+x\right)-\frac{1}{3}x\left(3x^{2}+6x\right)$$

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

$$x^{3}-x^{2}-x+3x^{2}+3x-\frac{1}{3}x\left(3x^{2}+6x\right)$$

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

$$x^{3}+2x^{2}-x+3x-\frac{1}{3}x\left(3x^{2}+6x\right)$$

Combine -x and 3x to get 2x.

$$x^{3}+2x^{2}+2x-\frac{1}{3}x\left(3x^{2}+6x\right)$$

Use the distributive property to multiply -\frac{1}{3}x by 3x^{2}+6x.

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

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

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

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

$$2x$$

Expand

$$2x$$

Solution Steps

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

$$x^{3}-x^{2}-x+3\left(x^{2}+x\right)-\frac{1}{3}x\left(3x^{2}+6x\right)$$

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

$$x^{3}-x^{2}-x+3x^{2}+3x-\frac{1}{3}x\left(3x^{2}+6x\right)$$

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

$$x^{3}+2x^{2}-x+3x-\frac{1}{3}x\left(3x^{2}+6x\right)$$

Combine -x and 3x to get 2x.

$$x^{3}+2x^{2}+2x-\frac{1}{3}x\left(3x^{2}+6x\right)$$

Use the distributive property to multiply -\frac{1}{3}x by 3x^{2}+6x.

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

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

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

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

$$2x$$