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

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

Expand

$$36x^{4}+54x^{3}+26x^{2}+4x$$

Solution Steps

Use the distributive property to multiply 2x by 2x+1.

$$\left(4x^{2}+2x\right)\left(3x+1\right)\left(3x+2\right)$$

Apply the distributive property by multiplying each term of 4x^{2}+2x by each term of 3x+1.

$$\left(12x^{3}+4x^{2}+6x^{2}+2x\right)\left(3x+2\right)$$

Combine 4x^{2} and 6x^{2} to get 10x^{2}.

$$\left(12x^{3}+10x^{2}+2x\right)\left(3x+2\right)$$

Apply the distributive property by multiplying each term of 12x^{3}+10x^{2}+2x by each term of 3x+2.

$$36x^{4}+24x^{3}+30x^{3}+20x^{2}+6x^{2}+4x$$

Combine 24x^{3} and 30x^{3} to get 54x^{3}.

$$36x^{4}+54x^{3}+20x^{2}+6x^{2}+4x$$

Combine 20x^{2} and 6x^{2} to get 26x^{2}.

$$36x^{4}+54x^{3}+26x^{2}+4x$$

Evaluate

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

Solution Steps

Use the distributive property to multiply 2x by 2x+1.

$$\left(4x^{2}+2x\right)\left(3x+1\right)\left(3x+2\right)$$

Apply the distributive property by multiplying each term of 4x^{2}+2x by each term of 3x+1.

$$\left(12x^{3}+4x^{2}+6x^{2}+2x\right)\left(3x+2\right)$$

Combine 4x^{2} and 6x^{2} to get 10x^{2}.

$$\left(12x^{3}+10x^{2}+2x\right)\left(3x+2\right)$$

Apply the distributive property by multiplying each term of 12x^{3}+10x^{2}+2x by each term of 3x+2.

$$36x^{4}+24x^{3}+30x^{3}+20x^{2}+6x^{2}+4x$$

Combine 24x^{3} and 30x^{3} to get 54x^{3}.

$$36x^{4}+54x^{3}+20x^{2}+6x^{2}+4x$$

Combine 20x^{2} and 6x^{2} to get 26x^{2}.

$$36x^{4}+54x^{3}+26x^{2}+4x$$