Solve 3(v+4)(v-3)(v-2)

$$3 ( v + 4 ) ( v - 3 ) ( v - 2 )$$

Evaluate

$$3\left(v-3\right)\left(v-2\right)\left(v+4\right)$$

Solution Steps

Use the distributive property to multiply 3 by v+4.

$$\left(3v+12\right)\left(v-3\right)\left(v-2\right)$$

Apply the distributive property by multiplying each term of 3v+12 by each term of v-3.

$$\left(3v^{2}-9v+12v-36\right)\left(v-2\right)$$

Combine -9v and 12v to get 3v.

$$\left(3v^{2}+3v-36\right)\left(v-2\right)$$

Apply the distributive property by multiplying each term of 3v^{2}+3v-36 by each term of v-2.

$$3v^{3}-6v^{2}+3v^{2}-6v-36v+72$$

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

$$3v^{3}-3v^{2}-6v-36v+72$$

Combine -6v and -36v to get -42v.

$$3v^{3}-3v^{2}-42v+72$$

Expand

$$3v^{3}-3v^{2}-42v+72$$

Solution Steps

Use the distributive property to multiply 3 by v+4.

$$\left(3v+12\right)\left(v-3\right)\left(v-2\right)$$

Apply the distributive property by multiplying each term of 3v+12 by each term of v-3.

$$\left(3v^{2}-9v+12v-36\right)\left(v-2\right)$$

Combine -9v and 12v to get 3v.

$$\left(3v^{2}+3v-36\right)\left(v-2\right)$$

Apply the distributive property by multiplying each term of 3v^{2}+3v-36 by each term of v-2.

$$3v^{3}-6v^{2}+3v^{2}-6v-36v+72$$

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

$$3v^{3}-3v^{2}-6v-36v+72$$

Combine -6v and -36v to get -42v.

$$3v^{3}-3v^{2}-42v+72$$