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

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

Evaluate

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

Solution Steps

Apply the distributive property by multiplying each term of x+2 by each term of x-1.

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

Combine -x and 2x to get x.

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

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

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

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

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

Combine x and -2x to get -x.

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

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

$$3x^{4}+x^{3}+6x^{3}+2x^{2}-3x^{2}-x-6x-2$$

Combine x^{3} and 6x^{3} to get 7x^{3}.

$$3x^{4}+7x^{3}+2x^{2}-3x^{2}-x-6x-2$$

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

$$3x^{4}+7x^{3}-x^{2}-x-6x-2$$

Combine -x and -6x to get -7x.

$$3x^{4}+7x^{3}-x^{2}-7x-2$$

Expand

$$3x^{4}+7x^{3}-x^{2}-7x-2$$

Solution Steps

Apply the distributive property by multiplying each term of x+2 by each term of x-1.

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

Combine -x and 2x to get x.

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

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

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

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

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

Combine x and -2x to get -x.

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

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

$$3x^{4}+x^{3}+6x^{3}+2x^{2}-3x^{2}-x-6x-2$$

Combine x^{3} and 6x^{3} to get 7x^{3}.

$$3x^{4}+7x^{3}+2x^{2}-3x^{2}-x-6x-2$$

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

$$3x^{4}+7x^{3}-x^{2}-x-6x-2$$

Combine -x and -6x to get -7x.

$$3x^{4}+7x^{3}-x^{2}-7x-2$$