Solve -7x(x-3)-(4-3x)(2x-2)

$$-7x(x-3)-(4-3x)(2x-2)$$

Evaluate

$$-\left(x-8\right)\left(x+1\right)$$

Solution Steps

Use the distributive property to multiply -7x by x-3.

$$-7x^{2}+21x-\left(4-3x\right)\left(2x-2\right)$$

Apply the distributive property by multiplying each term of 4-3x by each term of 2x-2.

$$-7x^{2}+21x-\left(8x-8-6x^{2}+6x\right)$$

Combine 8x and 6x to get 14x.

$$-7x^{2}+21x-\left(14x-8-6x^{2}\right)$$

To find the opposite of 14x-8-6x^{2}, find the opposite of each term.

$$-7x^{2}+21x-14x-\left(-8\right)-\left(-6x^{2}\right)$$

The opposite of -8 is 8.

$$-7x^{2}+21x-14x+8-\left(-6x^{2}\right)$$

The opposite of -6x^{2} is 6x^{2}.

$$-7x^{2}+21x-14x+8+6x^{2}$$

Combine 21x and -14x to get 7x.

$$-7x^{2}+7x+8+6x^{2}$$

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

$$-x^{2}+7x+8$$

Expand

$$8+7x-x^{2}$$

Solution Steps

Use the distributive property to multiply -7x by x-3.

$$-7x^{2}+21x-\left(4-3x\right)\left(2x-2\right)$$

Apply the distributive property by multiplying each term of 4-3x by each term of 2x-2.

$$-7x^{2}+21x-\left(8x-8-6x^{2}+6x\right)$$

Combine 8x and 6x to get 14x.

$$-7x^{2}+21x-\left(14x-8-6x^{2}\right)$$

To find the opposite of 14x-8-6x^{2}, find the opposite of each term.

$$-7x^{2}+21x-14x-\left(-8\right)-\left(-6x^{2}\right)$$

The opposite of -8 is 8.

$$-7x^{2}+21x-14x+8-\left(-6x^{2}\right)$$

The opposite of -6x^{2} is 6x^{2}.

$$-7x^{2}+21x-14x+8+6x^{2}$$

Combine 21x and -14x to get 7x.

$$-7x^{2}+7x+8+6x^{2}$$

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

$$-x^{2}+7x+8$$