Solve xleft(x+1right)^2(x-2)(x-2)

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

Evaluate

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

Solution Steps

Multiply x-2 and x-2 to get \left(x-2\right)^{2}.

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

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

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

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

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

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

$$\left(x^{3}+2x^{2}+x\right)\left(x^{2}-4x+4\right)$$

Use the distributive property to multiply x^{3}+2x^{2}+x by x^{2}-4x+4 and combine like terms.

$$x^{5}-2x^{4}-3x^{3}+4x^{2}+4x$$

Expand

$$x^{5}-2x^{4}-3x^{3}+4x^{2}+4x$$

Solution Steps

Multiply x-2 and x-2 to get \left(x-2\right)^{2}.

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

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

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

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

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

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

$$\left(x^{3}+2x^{2}+x\right)\left(x^{2}-4x+4\right)$$

Use the distributive property to multiply x^{3}+2x^{2}+x by x^{2}-4x+4 and combine like terms.

$$x^{5}-2x^{4}-3x^{3}+4x^{2}+4x$$