Solve 12x(x-3)(x-2)(x+1)

$$12x(x-3)(x-2)(x+1)$$

Expand

$$12x^{4}-48x^{3}+12x^{2}+72x$$

Solution Steps

Use the distributive property to multiply 12x by x-3.

$$\left(12x^{2}-36x\right)\left(x-2\right)\left(x+1\right)$$

Apply the distributive property by multiplying each term of 12x^{2}-36x by each term of x-2.

$$\left(12x^{3}-24x^{2}-36x^{2}+72x\right)\left(x+1\right)$$

Combine -24x^{2} and -36x^{2} to get -60x^{2}.

$$\left(12x^{3}-60x^{2}+72x\right)\left(x+1\right)$$

Apply the distributive property by multiplying each term of 12x^{3}-60x^{2}+72x by each term of x+1.

$$12x^{4}+12x^{3}-60x^{3}-60x^{2}+72x^{2}+72x$$

Combine 12x^{3} and -60x^{3} to get -48x^{3}.

$$12x^{4}-48x^{3}-60x^{2}+72x^{2}+72x$$

Combine -60x^{2} and 72x^{2} to get 12x^{2}.

$$12x^{4}-48x^{3}+12x^{2}+72x$$

Evaluate

$$12x\left(x-3\right)\left(x-2\right)\left(x+1\right)$$

Solution Steps

Use the distributive property to multiply 12x by x-3.

$$\left(12x^{2}-36x\right)\left(x-2\right)\left(x+1\right)$$

Apply the distributive property by multiplying each term of 12x^{2}-36x by each term of x-2.

$$\left(12x^{3}-24x^{2}-36x^{2}+72x\right)\left(x+1\right)$$

Combine -24x^{2} and -36x^{2} to get -60x^{2}.

$$\left(12x^{3}-60x^{2}+72x\right)\left(x+1\right)$$

Apply the distributive property by multiplying each term of 12x^{3}-60x^{2}+72x by each term of x+1.

$$12x^{4}+12x^{3}-60x^{3}-60x^{2}+72x^{2}+72x$$

Combine 12x^{3} and -60x^{3} to get -48x^{3}.

$$12x^{4}-48x^{3}-60x^{2}+72x^{2}+72x$$

Combine -60x^{2} and 72x^{2} to get 12x^{2}.

$$12x^{4}-48x^{3}+12x^{2}+72x$$