Solve (x-1)(x+1)(x-2)(x+2)-40

$$( x - 1 ) ( x + 1 ) ( x - 2 ) ( x + 2 ) - 40$$

Evaluate

$$x^{4}-5x^{2}-36$$

Solution Steps

Apply the distributive property by multiplying each term of x-1 by each term of x+1.

$$\left(x^{2}+x-x-1\right)\left(x-2\right)\left(x+2\right)-40$$

Combine x and -x to get 0.

$$\left(x^{2}-1\right)\left(x-2\right)\left(x+2\right)-40$$

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

$$\left(x^{3}-2x^{2}-x+2\right)\left(x+2\right)-40$$

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

$$x^{4}+2x^{3}-2x^{3}-4x^{2}-x^{2}-2x+2x+4-40$$

Combine 2x^{3} and -2x^{3} to get 0.

$$x^{4}-4x^{2}-x^{2}-2x+2x+4-40$$

Combine -4x^{2} and -x^{2} to get -5x^{2}.

$$x^{4}-5x^{2}-2x+2x+4-40$$

Combine -2x and 2x to get 0.

$$x^{4}-5x^{2}+4-40$$

Subtract 40 from 4 to get -36.

$$x^{4}-5x^{2}-36$$

Expand

$$x^{4}-5x^{2}-36$$

Solution Steps

Apply the distributive property by multiplying each term of x-1 by each term of x+1.

$$\left(x^{2}+x-x-1\right)\left(x-2\right)\left(x+2\right)-40$$

Combine x and -x to get 0.

$$\left(x^{2}-1\right)\left(x-2\right)\left(x+2\right)-40$$

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

$$\left(x^{3}-2x^{2}-x+2\right)\left(x+2\right)-40$$

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

$$x^{4}+2x^{3}-2x^{3}-4x^{2}-x^{2}-2x+2x+4-40$$

Combine 2x^{3} and -2x^{3} to get 0.

$$x^{4}-4x^{2}-x^{2}-2x+2x+4-40$$

Combine -4x^{2} and -x^{2} to get -5x^{2}.

$$x^{4}-5x^{2}-2x+2x+4-40$$

Combine -2x and 2x to get 0.

$$x^{4}-5x^{2}+4-40$$

Subtract 40 from 4 to get -36.

$$x^{4}-5x^{2}-36$$