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

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

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+2.

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

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

$$\left(x^{3}-4x^{2}+2x^{2}-8x\right)\left(x-6\right)$$

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

$$\left(x^{3}-2x^{2}-8x\right)\left(x-6\right)$$

Apply the distributive property by multiplying each term of x^{3}-2x^{2}-8x by each term of x-6.

$$x^{4}-6x^{3}-2x^{3}+12x^{2}-8x^{2}+48x$$

Combine -6x^{3} and -2x^{3} to get -8x^{3}.

$$x^{4}-8x^{3}+12x^{2}-8x^{2}+48x$$

Combine 12x^{2} and -8x^{2} to get 4x^{2}.

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

Expand

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

Solution Steps

Use the distributive property to multiply x by x+2.

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

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

$$\left(x^{3}-4x^{2}+2x^{2}-8x\right)\left(x-6\right)$$

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

$$\left(x^{3}-2x^{2}-8x\right)\left(x-6\right)$$

Apply the distributive property by multiplying each term of x^{3}-2x^{2}-8x by each term of x-6.

$$x^{4}-6x^{3}-2x^{3}+12x^{2}-8x^{2}+48x$$

Combine -6x^{3} and -2x^{3} to get -8x^{3}.

$$x^{4}-8x^{3}+12x^{2}-8x^{2}+48x$$

Combine 12x^{2} and -8x^{2} to get 4x^{2}.

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