Solve (x-6)(2-x)-(2-x)(3+4x)

$$( x - 6 ) ( 2 - x ) - ( 2 - x ) ( 3 + 4 x )$$

Evaluate

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

Solution Steps

Apply the distributive property by multiplying each term of x-6 by each term of 2-x.

$$2x-x^{2}-12+6x-\left(2-x\right)\left(3+4x\right)$$

Combine 2x and 6x to get 8x.

$$8x-x^{2}-12-\left(2-x\right)\left(3+4x\right)$$

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

$$8x-x^{2}-12-\left(6+8x-3x-4x^{2}\right)$$

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

$$8x-x^{2}-12-\left(6+5x-4x^{2}\right)$$

To find the opposite of 6+5x-4x^{2}, find the opposite of each term.

$$8x-x^{2}-12-6-5x-\left(-4x^{2}\right)$$

The opposite of -4x^{2} is 4x^{2}.

$$8x-x^{2}-12-6-5x+4x^{2}$$

Subtract 6 from -12 to get -18.

$$8x-x^{2}-18-5x+4x^{2}$$

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

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

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

$$3x+3x^{2}-18$$

Expand

$$3x^{2}+3x-18$$

Solution Steps

Apply the distributive property by multiplying each term of x-6 by each term of 2-x.

$$2x-x^{2}-12+6x-\left(2-x\right)\left(3+4x\right)$$

Combine 2x and 6x to get 8x.

$$8x-x^{2}-12-\left(2-x\right)\left(3+4x\right)$$

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

$$8x-x^{2}-12-\left(6+8x-3x-4x^{2}\right)$$

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

$$8x-x^{2}-12-\left(6+5x-4x^{2}\right)$$

To find the opposite of 6+5x-4x^{2}, find the opposite of each term.

$$8x-x^{2}-12-6-5x-\left(-4x^{2}\right)$$

The opposite of -4x^{2} is 4x^{2}.

$$8x-x^{2}-12-6-5x+4x^{2}$$

Subtract 6 from -12 to get -18.

$$8x-x^{2}-18-5x+4x^{2}$$

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

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

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

$$3x+3x^{2}-18$$