Solve (3x-6left(x+3right)-left(-x+2right)left(x-3right)

$$(3x-6 \left( x+3 \right) - \left( -x+2 \right) \left( x-3 \right)$$

Evaluate

$$x^{2}-8x-12$$

Solution Steps

Use the distributive property to multiply -6 by x+3.

$$3x-6x-18-\left(-x+2\right)\left(x-3\right)$$

Combine 3x and -6x to get -3x.

$$-3x-18-\left(-x+2\right)\left(x-3\right)$$

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

$$-3x-18-\left(\left(-x\right)x-3\left(-x\right)+2x-6\right)$$

Multiply -3 and -1 to get 3.

$$-3x-18-\left(\left(-x\right)x+3x+2x-6\right)$$

Combine 3x and 2x to get 5x.

$$-3x-18-\left(\left(-x\right)x+5x-6\right)$$

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

$$-3x-18-\left(-x\right)x-5x-\left(-6\right)$$

Multiply -1 and -1 to get 1.

$$-3x-18+xx-5x-\left(-6\right)$$

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

$$-3x-18+x^{2}-5x-\left(-6\right)$$

Combine -3x and -5x to get -8x.

$$-8x-18+x^{2}-\left(-6\right)$$

The opposite of -6 is 6.

$$-8x-18+x^{2}+6$$

Add -18 and 6 to get -12.

$$-8x-12+x^{2}$$

Expand

$$x^{2}-8x-12$$

Solution Steps

Use the distributive property to multiply -6 by x+3.

$$3x-6x-18-\left(-x+2\right)\left(x-3\right)$$

Combine 3x and -6x to get -3x.

$$-3x-18-\left(-x+2\right)\left(x-3\right)$$

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

$$-3x-18-\left(\left(-x\right)x-3\left(-x\right)+2x-6\right)$$

Multiply -3 and -1 to get 3.

$$-3x-18-\left(\left(-x\right)x+3x+2x-6\right)$$

Combine 3x and 2x to get 5x.

$$-3x-18-\left(\left(-x\right)x+5x-6\right)$$

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

$$-3x-18-\left(-x\right)x-5x-\left(-6\right)$$

Multiply -1 and -1 to get 1.

$$-3x-18+xx-5x-\left(-6\right)$$

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

$$-3x-18+x^{2}-5x-\left(-6\right)$$

Combine -3x and -5x to get -8x.

$$-8x-18+x^{2}-\left(-6\right)$$

The opposite of -6 is 6.

$$-8x-18+x^{2}+6$$

Add -18 and 6 to get -12.

$$-8x-12+x^{2}$$