Solve left(-x+2right)left(4+xright)-3left(4-xright)left(x+3right)

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

Evaluate

$$2x^{2}-5x-28$$

Solution Steps

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

$$4\left(-x\right)+\left(-x\right)x+8+2x-3\left(4-x\right)\left(x+3\right)$$

Multiply 4 and -1 to get -4.

$$-4x-xx+8+2x-3\left(4-x\right)\left(x+3\right)$$

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

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

Combine -4x and 2x to get -2x.

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

Use the distributive property to multiply -3 by 4-x.

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

Apply the distributive property by multiplying each term of -12+3x by each term of x+3.

$$-2x-x^{2}+8-12x-36+3x^{2}+9x$$

Combine -12x and 9x to get -3x.

$$-2x-x^{2}+8-3x-36+3x^{2}$$

Combine -2x and -3x to get -5x.

$$-5x-x^{2}+8-36+3x^{2}$$

Subtract 36 from 8 to get -28.

$$-5x-x^{2}-28+3x^{2}$$

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

$$-5x+2x^{2}-28$$

Expand

$$2x^{2}-5x-28$$

Solution Steps

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

$$4\left(-x\right)+\left(-x\right)x+8+2x-3\left(4-x\right)\left(x+3\right)$$

Multiply 4 and -1 to get -4.

$$-4x-xx+8+2x-3\left(4-x\right)\left(x+3\right)$$

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

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

Combine -4x and 2x to get -2x.

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

Use the distributive property to multiply -3 by 4-x.

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

Apply the distributive property by multiplying each term of -12+3x by each term of x+3.

$$-2x-x^{2}+8-12x-36+3x^{2}+9x$$

Combine -12x and 9x to get -3x.

$$-2x-x^{2}+8-3x-36+3x^{2}$$

Combine -2x and -3x to get -5x.

$$-5x-x^{2}+8-36+3x^{2}$$

Subtract 36 from 8 to get -28.

$$-5x-x^{2}-28+3x^{2}$$

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

$$-5x+2x^{2}-28$$