Solve left(x+5right)left(x-5right)(x-1)left(x-2right)

$$\left( x+5 \right) \left( x-5 \right) (x-1) \left( x-2 \right)$$

Evaluate

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

Solution Steps

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

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

Combine -5x and 5x to get 0.

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

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

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

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

$$x^{4}-2x^{3}-x^{3}+2x^{2}-25x^{2}+50x+25x-50$$

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

$$x^{4}-3x^{3}+2x^{2}-25x^{2}+50x+25x-50$$

Combine 2x^{2} and -25x^{2} to get -23x^{2}.

$$x^{4}-3x^{3}-23x^{2}+50x+25x-50$$

Combine 50x and 25x to get 75x.

$$x^{4}-3x^{3}-23x^{2}+75x-50$$

Expand

$$x^{4}-3x^{3}-23x^{2}+75x-50$$

Solution Steps

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

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

Combine -5x and 5x to get 0.

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

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

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

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

$$x^{4}-2x^{3}-x^{3}+2x^{2}-25x^{2}+50x+25x-50$$

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

$$x^{4}-3x^{3}+2x^{2}-25x^{2}+50x+25x-50$$

Combine 2x^{2} and -25x^{2} to get -23x^{2}.

$$x^{4}-3x^{3}-23x^{2}+50x+25x-50$$

Combine 50x and 25x to get 75x.

$$x^{4}-3x^{3}-23x^{2}+75x-50$$