Solve x(x-4)^3

$$x ( x - 4 ) ^ { 3 }$$

Expand

$$x^{4}-12x^{3}+48x^{2}-64x$$

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(x-4\right)^{3}.

$$x\left(x^{3}-12x^{2}+48x-64\right)$$

Use the distributive property to multiply x by x^{3}-12x^{2}+48x-64.

$$x^{4}-12x^{3}+48x^{2}-64x$$

Evaluate

$$x\left(x-4\right)^{3}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(x-4\right)^{3}.

$$x\left(x^{3}-12x^{2}+48x-64\right)$$

Use the distributive property to multiply x by x^{3}-12x^{2}+48x-64.

$$x^{4}-12x^{3}+48x^{2}-64x$$