Solve (x-1)(x+1)(x+3)(x-3)

$$( x - 1 ) ( x + 1 ) ( x + 3 ) ( x - 3 )$$

Evaluate

$$x^{4}-10x^{2}+9$$

Solution Steps

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

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

Combine x and -x to get 0.

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

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

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

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

$$x^{4}-3x^{3}+3x^{3}-9x^{2}-x^{2}+3x-3x+9$$

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

$$x^{4}-9x^{2}-x^{2}+3x-3x+9$$

Combine -9x^{2} and -x^{2} to get -10x^{2}.

$$x^{4}-10x^{2}+3x-3x+9$$

Combine 3x and -3x to get 0.

$$x^{4}-10x^{2}+9$$

Expand

$$x^{4}-10x^{2}+9$$

Solution Steps

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

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

Combine x and -x to get 0.

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

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

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

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

$$x^{4}-3x^{3}+3x^{3}-9x^{2}-x^{2}+3x-3x+9$$

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

$$x^{4}-9x^{2}-x^{2}+3x-3x+9$$

Combine -9x^{2} and -x^{2} to get -10x^{2}.

$$x^{4}-10x^{2}+3x-3x+9$$

Combine 3x and -3x to get 0.

$$x^{4}-10x^{2}+9$$