Solve (x+4)(x+1)(x-1)(x-4)

$$( x + 4 ) ( x + 1 ) ( x - 1 ) ( x - 4 )$$

Evaluate

$$x^{4}-17x^{2}+16$$

Solution Steps

Apply the distributive property by multiplying each term of x+4 by each term of x+1.

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

Combine x and 4x to get 5x.

$$\left(x^{2}+5x+4\right)\left(x-1\right)\left(x-4\right)$$

Apply the distributive property by multiplying each term of x^{2}+5x+4 by each term of x-1.

$$\left(x^{3}-x^{2}+5x^{2}-5x+4x-4\right)\left(x-4\right)$$

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

$$\left(x^{3}+4x^{2}-5x+4x-4\right)\left(x-4\right)$$

Combine -5x and 4x to get -x.

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

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

$$x^{4}-4x^{3}+4x^{3}-16x^{2}-x^{2}+4x-4x+16$$

Combine -4x^{3} and 4x^{3} to get 0.

$$x^{4}-16x^{2}-x^{2}+4x-4x+16$$

Combine -16x^{2} and -x^{2} to get -17x^{2}.

$$x^{4}-17x^{2}+4x-4x+16$$

Combine 4x and -4x to get 0.

$$x^{4}-17x^{2}+16$$

Expand

$$x^{4}-17x^{2}+16$$

Solution Steps

Apply the distributive property by multiplying each term of x+4 by each term of x+1.

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

Combine x and 4x to get 5x.

$$\left(x^{2}+5x+4\right)\left(x-1\right)\left(x-4\right)$$

Apply the distributive property by multiplying each term of x^{2}+5x+4 by each term of x-1.

$$\left(x^{3}-x^{2}+5x^{2}-5x+4x-4\right)\left(x-4\right)$$

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

$$\left(x^{3}+4x^{2}-5x+4x-4\right)\left(x-4\right)$$

Combine -5x and 4x to get -x.

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

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

$$x^{4}-4x^{3}+4x^{3}-16x^{2}-x^{2}+4x-4x+16$$

Combine -4x^{3} and 4x^{3} to get 0.

$$x^{4}-16x^{2}-x^{2}+4x-4x+16$$

Combine -16x^{2} and -x^{2} to get -17x^{2}.

$$x^{4}-17x^{2}+4x-4x+16$$

Combine 4x and -4x to get 0.

$$x^{4}-17x^{2}+16$$