Solve x(4x-1)(x+1)-(-x+3)(x-2)

$$x(4x-1)(x+1)-(-x+3)(x-2)$$

Evaluate

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

Solution Steps

Use the distributive property to multiply x by 4x-1.

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

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

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

Combine 4x^{2} and -x^{2} to get 3x^{2}.

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

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

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

Multiply -2 and -1 to get 2.

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

Combine 2x and 3x to get 5x.

$$4x^{3}+3x^{2}-x-\left(\left(-x\right)x+5x-6\right)$$

To find the opposite of \left(-x\right)x+5x-6, find the opposite of each term.

$$4x^{3}+3x^{2}-x-\left(-x\right)x-5x-\left(-6\right)$$

Multiply -1 and -1 to get 1.

$$4x^{3}+3x^{2}-x+xx-5x-\left(-6\right)$$

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

$$4x^{3}+3x^{2}-x+x^{2}-5x-\left(-6\right)$$

Combine 3x^{2} and x^{2} to get 4x^{2}.

$$4x^{3}+4x^{2}-x-5x-\left(-6\right)$$

Combine -x and -5x to get -6x.

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

The opposite of -6 is 6.

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

Expand

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

Solution Steps

Use the distributive property to multiply x by 4x-1.

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

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

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

Combine 4x^{2} and -x^{2} to get 3x^{2}.

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

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

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

Multiply -2 and -1 to get 2.

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

Combine 2x and 3x to get 5x.

$$4x^{3}+3x^{2}-x-\left(\left(-x\right)x+5x-6\right)$$

To find the opposite of \left(-x\right)x+5x-6, find the opposite of each term.

$$4x^{3}+3x^{2}-x-\left(-x\right)x-5x-\left(-6\right)$$

Multiply -1 and -1 to get 1.

$$4x^{3}+3x^{2}-x+xx-5x-\left(-6\right)$$

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

$$4x^{3}+3x^{2}-x+x^{2}-5x-\left(-6\right)$$

Combine 3x^{2} and x^{2} to get 4x^{2}.

$$4x^{3}+4x^{2}-x-5x-\left(-6\right)$$

Combine -x and -5x to get -6x.

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

The opposite of -6 is 6.

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