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

$$(x+1)(x-1)(x+2)(x-1)$$

Evaluate

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

Solution Steps

Multiply x-1 and x-1 to get \left(x-1\right)^{2}.

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

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

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

Apply the distributive property by multiplying each term of x+1 by each term of x^{2}-2x+1.

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

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

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

Combine x and -2x to get -x.

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

Apply the distributive property by multiplying each term of x^{3}-x^{2}-x+1 by each term of x+2.

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

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

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

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

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

Combine -2x and x to get -x.

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

Expand

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

Solution Steps

Multiply x-1 and x-1 to get \left(x-1\right)^{2}.

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

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

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

Apply the distributive property by multiplying each term of x+1 by each term of x^{2}-2x+1.

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

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

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

Combine x and -2x to get -x.

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

Apply the distributive property by multiplying each term of x^{3}-x^{2}-x+1 by each term of x+2.

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

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

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

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

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

Combine -2x and x to get -x.

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