Solve x(x-6)(x-4)(x+2)

$$x ( x - 6 ) ( x - 4 ) ( x + 2 )$$

Expand

$$x^{4}-8x^{3}+4x^{2}+48x$$

Solution Steps

Use the distributive property to multiply x by x-6.

$$\left(x^{2}-6x\right)\left(x-4\right)\left(x+2\right)$$

Apply the distributive property by multiplying each term of x^{2}-6x by each term of x-4.

$$\left(x^{3}-4x^{2}-6x^{2}+24x\right)\left(x+2\right)$$

Combine -4x^{2} and -6x^{2} to get -10x^{2}.

$$\left(x^{3}-10x^{2}+24x\right)\left(x+2\right)$$

Apply the distributive property by multiplying each term of x^{3}-10x^{2}+24x by each term of x+2.

$$x^{4}+2x^{3}-10x^{3}-20x^{2}+24x^{2}+48x$$

Combine 2x^{3} and -10x^{3} to get -8x^{3}.

$$x^{4}-8x^{3}-20x^{2}+24x^{2}+48x$$

Combine -20x^{2} and 24x^{2} to get 4x^{2}.

$$x^{4}-8x^{3}+4x^{2}+48x$$

Evaluate

$$x\left(x-6\right)\left(x-4\right)\left(x+2\right)$$

Solution Steps

Use the distributive property to multiply x by x-6.

$$\left(x^{2}-6x\right)\left(x-4\right)\left(x+2\right)$$

Apply the distributive property by multiplying each term of x^{2}-6x by each term of x-4.

$$\left(x^{3}-4x^{2}-6x^{2}+24x\right)\left(x+2\right)$$

Combine -4x^{2} and -6x^{2} to get -10x^{2}.

$$\left(x^{3}-10x^{2}+24x\right)\left(x+2\right)$$

Apply the distributive property by multiplying each term of x^{3}-10x^{2}+24x by each term of x+2.

$$x^{4}+2x^{3}-10x^{3}-20x^{2}+24x^{2}+48x$$

Combine 2x^{3} and -10x^{3} to get -8x^{3}.

$$x^{4}-8x^{3}-20x^{2}+24x^{2}+48x$$

Combine -20x^{2} and 24x^{2} to get 4x^{2}.

$$x^{4}-8x^{3}+4x^{2}+48x$$