Solve x(x-4)^2(x+1)

$$x ( x - 4 ) ^ { 2 } ( x + 1 )$$

Evaluate

$$x\left(x+1\right)\left(x-4\right)^{2}$$

Solution Steps

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

$$x\left(x^{2}-8x+16\right)\left(x+1\right)$$

Use the distributive property to multiply x by x^{2}-8x+16.

$$\left(x^{3}-8x^{2}+16x\right)\left(x+1\right)$$

Use the distributive property to multiply x^{3}-8x^{2}+16x by x+1 and combine like terms.

$$x^{4}-7x^{3}+8x^{2}+16x$$

Expand

$$x^{4}-7x^{3}+8x^{2}+16x$$

Solution Steps

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

$$x\left(x^{2}-8x+16\right)\left(x+1\right)$$

Use the distributive property to multiply x by x^{2}-8x+16.

$$\left(x^{3}-8x^{2}+16x\right)\left(x+1\right)$$

Use the distributive property to multiply x^{3}-8x^{2}+16x by x+1 and combine like terms.

$$x^{4}-7x^{3}+8x^{2}+16x$$