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

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

Evaluate

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

Solution Steps

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

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

Combine -x and 2x to get x.

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

Use the distributive property to multiply x^{2}+x-2 by 3.

$$\left(3x^{2}+3x-6\right)x\left(3x+1\right)$$

Use the distributive property to multiply 3x^{2}+3x-6 by x.

$$\left(3x^{3}+3x^{2}-6x\right)\left(3x+1\right)$$

Apply the distributive property by multiplying each term of 3x^{3}+3x^{2}-6x by each term of 3x+1.

$$9x^{4}+3x^{3}+9x^{3}+3x^{2}-18x^{2}-6x$$

Combine 3x^{3} and 9x^{3} to get 12x^{3}.

$$9x^{4}+12x^{3}+3x^{2}-18x^{2}-6x$$

Combine 3x^{2} and -18x^{2} to get -15x^{2}.

$$9x^{4}+12x^{3}-15x^{2}-6x$$

Expand

$$9x^{4}+12x^{3}-15x^{2}-6x$$

Solution Steps

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

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

Combine -x and 2x to get x.

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

Use the distributive property to multiply x^{2}+x-2 by 3.

$$\left(3x^{2}+3x-6\right)x\left(3x+1\right)$$

Use the distributive property to multiply 3x^{2}+3x-6 by x.

$$\left(3x^{3}+3x^{2}-6x\right)\left(3x+1\right)$$

Apply the distributive property by multiplying each term of 3x^{3}+3x^{2}-6x by each term of 3x+1.

$$9x^{4}+3x^{3}+9x^{3}+3x^{2}-18x^{2}-6x$$

Combine 3x^{3} and 9x^{3} to get 12x^{3}.

$$9x^{4}+12x^{3}+3x^{2}-18x^{2}-6x$$

Combine 3x^{2} and -18x^{2} to get -15x^{2}.

$$9x^{4}+12x^{3}-15x^{2}-6x$$