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

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

Evaluate

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

Solution Steps

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

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

Combine 2x and -3x to get -x.

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

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

$$\left(3x^{3}-6x^{2}-x^{2}+2x-2x+4\right)\left(2x+1\right)$$

Combine -6x^{2} and -x^{2} to get -7x^{2}.

$$\left(3x^{3}-7x^{2}+2x-2x+4\right)\left(2x+1\right)$$

Combine 2x and -2x to get 0.

$$\left(3x^{3}-7x^{2}+4\right)\left(2x+1\right)$$

Apply the distributive property by multiplying each term of 3x^{3}-7x^{2}+4 by each term of 2x+1.

$$6x^{4}+3x^{3}-14x^{3}-7x^{2}+8x+4$$

Combine 3x^{3} and -14x^{3} to get -11x^{3}.

$$6x^{4}-11x^{3}-7x^{2}+8x+4$$

Expand

$$6x^{4}-11x^{3}-7x^{2}+8x+4$$

Solution Steps

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

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

Combine 2x and -3x to get -x.

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

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

$$\left(3x^{3}-6x^{2}-x^{2}+2x-2x+4\right)\left(2x+1\right)$$

Combine -6x^{2} and -x^{2} to get -7x^{2}.

$$\left(3x^{3}-7x^{2}+2x-2x+4\right)\left(2x+1\right)$$

Combine 2x and -2x to get 0.

$$\left(3x^{3}-7x^{2}+4\right)\left(2x+1\right)$$

Apply the distributive property by multiplying each term of 3x^{3}-7x^{2}+4 by each term of 2x+1.

$$6x^{4}+3x^{3}-14x^{3}-7x^{2}+8x+4$$

Combine 3x^{3} and -14x^{3} to get -11x^{3}.

$$6x^{4}-11x^{3}-7x^{2}+8x+4$$