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

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

Evaluate

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

Solution Steps

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

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

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

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

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

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

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

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

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

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

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

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

Combine 2x^{4} and -2x^{4} to get 0.

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

Combine x^{3} and -4x^{3} to get -3x^{3}.

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

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

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

Combine -2x^{2} and 2x^{2} to get 0.

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

Expand

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

Solution Steps

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

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

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

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

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

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

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

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

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

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

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

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

Combine 2x^{4} and -2x^{4} to get 0.

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

Combine x^{3} and -4x^{3} to get -3x^{3}.

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

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

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

Combine -2x^{2} and 2x^{2} to get 0.

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