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

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

Evaluate

$$\left(x-1\right)\left(2x+1\right)\left(9x^{2}-1\right)$$

Solution Steps

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

$$\left(3x-1+9x^{2}-3x\right)\left(2x+1\right)\left(x-1\right)$$

Combine 3x and -3x to get 0.

$$\left(-1+9x^{2}\right)\left(2x+1\right)\left(x-1\right)$$

Apply the distributive property by multiplying each term of -1+9x^{2} by each term of 2x+1.

$$\left(-2x-1+18x^{3}+9x^{2}\right)\left(x-1\right)$$

Apply the distributive property by multiplying each term of -2x-1+18x^{3}+9x^{2} by each term of x-1.

$$-2x^{2}+2x-x+1+18x^{4}-18x^{3}+9x^{3}-9x^{2}$$

Combine 2x and -x to get x.

$$-2x^{2}+x+1+18x^{4}-18x^{3}+9x^{3}-9x^{2}$$

Combine -18x^{3} and 9x^{3} to get -9x^{3}.

$$-2x^{2}+x+1+18x^{4}-9x^{3}-9x^{2}$$

Combine -2x^{2} and -9x^{2} to get -11x^{2}.

$$-11x^{2}+x+1+18x^{4}-9x^{3}$$

Expand

$$18x^{4}-9x^{3}-11x^{2}+x+1$$

Solution Steps

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

$$\left(3x-1+9x^{2}-3x\right)\left(2x+1\right)\left(x-1\right)$$

Combine 3x and -3x to get 0.

$$\left(-1+9x^{2}\right)\left(2x+1\right)\left(x-1\right)$$

Apply the distributive property by multiplying each term of -1+9x^{2} by each term of 2x+1.

$$\left(-2x-1+18x^{3}+9x^{2}\right)\left(x-1\right)$$

Apply the distributive property by multiplying each term of -2x-1+18x^{3}+9x^{2} by each term of x-1.

$$-2x^{2}+2x-x+1+18x^{4}-18x^{3}+9x^{3}-9x^{2}$$

Combine 2x and -x to get x.

$$-2x^{2}+x+1+18x^{4}-18x^{3}+9x^{3}-9x^{2}$$

Combine -18x^{3} and 9x^{3} to get -9x^{3}.

$$-2x^{2}+x+1+18x^{4}-9x^{3}-9x^{2}$$

Combine -2x^{2} and -9x^{2} to get -11x^{2}.

$$-11x^{2}+x+1+18x^{4}-9x^{3}$$