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

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

Evaluate

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

Solution Steps

Apply the distributive property by multiplying each term of x-3 by each term of x-1.

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

Combine -x and -3x to get -4x.

$$\left(x^{2}-4x+3\right)\left(x+1\right)\left(x+3\right)$$

Apply the distributive property by multiplying each term of x^{2}-4x+3 by each term of x+1.

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

Combine x^{2} and -4x^{2} to get -3x^{2}.

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

Combine -4x and 3x to get -x.

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

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-3 by each term of x-1.

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

Combine -x and -3x to get -4x.

$$\left(x^{2}-4x+3\right)\left(x+1\right)\left(x+3\right)$$

Apply the distributive property by multiplying each term of x^{2}-4x+3 by each term of x+1.

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

Combine x^{2} and -4x^{2} to get -3x^{2}.

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

Combine -4x and 3x to get -x.

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

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.

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