Solve (x-4)(x+5)(x+4)(x-5)

$$( x - 4 ) ( x + 5 ) ( x + 4 ) ( x - 5 )$$

Evaluate

$$x^{4}-41x^{2}+400$$

Solution Steps

Apply the distributive property by multiplying each term of x-4 by each term of x+5.

$$\left(x^{2}+5x-4x-20\right)\left(x+4\right)\left(x-5\right)$$

Combine 5x and -4x to get x.

$$\left(x^{2}+x-20\right)\left(x+4\right)\left(x-5\right)$$

Apply the distributive property by multiplying each term of x^{2}+x-20 by each term of x+4.

$$\left(x^{3}+4x^{2}+x^{2}+4x-20x-80\right)\left(x-5\right)$$

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

$$\left(x^{3}+5x^{2}+4x-20x-80\right)\left(x-5\right)$$

Combine 4x and -20x to get -16x.

$$\left(x^{3}+5x^{2}-16x-80\right)\left(x-5\right)$$

Apply the distributive property by multiplying each term of x^{3}+5x^{2}-16x-80 by each term of x-5.

$$x^{4}-5x^{3}+5x^{3}-25x^{2}-16x^{2}+80x-80x+400$$

Combine -5x^{3} and 5x^{3} to get 0.

$$x^{4}-25x^{2}-16x^{2}+80x-80x+400$$

Combine -25x^{2} and -16x^{2} to get -41x^{2}.

$$x^{4}-41x^{2}+80x-80x+400$$

Combine 80x and -80x to get 0.

$$x^{4}-41x^{2}+400$$

Expand

$$x^{4}-41x^{2}+400$$

Solution Steps

Apply the distributive property by multiplying each term of x-4 by each term of x+5.

$$\left(x^{2}+5x-4x-20\right)\left(x+4\right)\left(x-5\right)$$

Combine 5x and -4x to get x.

$$\left(x^{2}+x-20\right)\left(x+4\right)\left(x-5\right)$$

Apply the distributive property by multiplying each term of x^{2}+x-20 by each term of x+4.

$$\left(x^{3}+4x^{2}+x^{2}+4x-20x-80\right)\left(x-5\right)$$

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

$$\left(x^{3}+5x^{2}+4x-20x-80\right)\left(x-5\right)$$

Combine 4x and -20x to get -16x.

$$\left(x^{3}+5x^{2}-16x-80\right)\left(x-5\right)$$

Apply the distributive property by multiplying each term of x^{3}+5x^{2}-16x-80 by each term of x-5.

$$x^{4}-5x^{3}+5x^{3}-25x^{2}-16x^{2}+80x-80x+400$$

Combine -5x^{3} and 5x^{3} to get 0.

$$x^{4}-25x^{2}-16x^{2}+80x-80x+400$$

Combine -25x^{2} and -16x^{2} to get -41x^{2}.

$$x^{4}-41x^{2}+80x-80x+400$$

Combine 80x and -80x to get 0.

$$x^{4}-41x^{2}+400$$