Solve (x+5)(x-5)(x+3)(x-1)=

$$( x + 5 ) ( x - 5 ) ( x + 3 ) ( x - 1 ) =$$

Evaluate

$$\left(x-1\right)\left(x+3\right)\left(x^{2}-25\right)$$

Solution Steps

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

$$\left(x^{2}-5x+5x-25\right)\left(x+3\right)\left(x-1\right)$$

Combine -5x and 5x to get 0.

$$\left(x^{2}-25\right)\left(x+3\right)\left(x-1\right)$$

Apply the distributive property by multiplying each term of x^{2}-25 by each term of x+3.

$$\left(x^{3}+3x^{2}-25x-75\right)\left(x-1\right)$$

Apply the distributive property by multiplying each term of x^{3}+3x^{2}-25x-75 by each term of x-1.

$$x^{4}-x^{3}+3x^{3}-3x^{2}-25x^{2}+25x-75x+75$$

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

$$x^{4}+2x^{3}-3x^{2}-25x^{2}+25x-75x+75$$

Combine -3x^{2} and -25x^{2} to get -28x^{2}.

$$x^{4}+2x^{3}-28x^{2}+25x-75x+75$$

Combine 25x and -75x to get -50x.

$$x^{4}+2x^{3}-28x^{2}-50x+75$$

Expand

$$x^{4}+2x^{3}-28x^{2}-50x+75$$

Solution Steps

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

$$\left(x^{2}-5x+5x-25\right)\left(x+3\right)\left(x-1\right)$$

Combine -5x and 5x to get 0.

$$\left(x^{2}-25\right)\left(x+3\right)\left(x-1\right)$$

Apply the distributive property by multiplying each term of x^{2}-25 by each term of x+3.

$$\left(x^{3}+3x^{2}-25x-75\right)\left(x-1\right)$$

Apply the distributive property by multiplying each term of x^{3}+3x^{2}-25x-75 by each term of x-1.

$$x^{4}-x^{3}+3x^{3}-3x^{2}-25x^{2}+25x-75x+75$$

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

$$x^{4}+2x^{3}-3x^{2}-25x^{2}+25x-75x+75$$

Combine -3x^{2} and -25x^{2} to get -28x^{2}.

$$x^{4}+2x^{3}-28x^{2}+25x-75x+75$$

Combine 25x and -75x to get -50x.

$$x^{4}+2x^{3}-28x^{2}-50x+75$$