Solve (x-5)(x-2)(x+8)

$$( x - 5 ) ( x - 2 ) ( x + 8 )$$

Expand

$$x^{3}+x^{2}-46x+80$$

Solution Steps

Apply the distributive property by multiplying each term of x-5 by each term of x-2.

$$\left(x^{2}-2x-5x+10\right)\left(x+8\right)$$

Combine -2x and -5x to get -7x.

$$\left(x^{2}-7x+10\right)\left(x+8\right)$$

Apply the distributive property by multiplying each term of x^{2}-7x+10 by each term of x+8.

$$x^{3}+8x^{2}-7x^{2}-56x+10x+80$$

Combine 8x^{2} and -7x^{2} to get x^{2}.

$$x^{3}+x^{2}-56x+10x+80$$

Combine -56x and 10x to get -46x.

$$x^{3}+x^{2}-46x+80$$

Evaluate

$$\left(x-5\right)\left(x-2\right)\left(x+8\right)$$

Solution Steps

Apply the distributive property by multiplying each term of x-5 by each term of x-2.

$$\left(x^{2}-2x-5x+10\right)\left(x+8\right)$$

Combine -2x and -5x to get -7x.

$$\left(x^{2}-7x+10\right)\left(x+8\right)$$

Apply the distributive property by multiplying each term of x^{2}-7x+10 by each term of x+8.

$$x^{3}+8x^{2}-7x^{2}-56x+10x+80$$

Combine 8x^{2} and -7x^{2} to get x^{2}.

$$x^{3}+x^{2}-56x+10x+80$$

Combine -56x and 10x to get -46x.

$$x^{3}+x^{2}-46x+80$$