Solve x(x-1)^3-8x=

$$x ( x - 1 ) ^ { 3 } - 8 x =$$

Evaluate

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

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(x-1\right)^{3}.

$$x\left(x^{3}-3x^{2}+3x-1\right)-8x$$

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

$$x^{4}-3x^{3}+3x^{2}-x-8x$$

Combine -x and -8x to get -9x.

$$x^{4}-3x^{3}+3x^{2}-9x$$

Expand

$$x^{4}-3x^{3}+3x^{2}-9x$$

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(x-1\right)^{3}.

$$x\left(x^{3}-3x^{2}+3x-1\right)-8x$$

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

$$x^{4}-3x^{3}+3x^{2}-x-8x$$

Combine -x and -8x to get -9x.

$$x^{4}-3x^{3}+3x^{2}-9x$$