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

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

Evaluate

$$16+3x-2x^{2}$$

Solution Steps

The opposite of -2 is 2.

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

The opposite of -3 is 3.

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

Use the distributive property to multiply 2 by x+2.

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

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

$$x+4+2x\left(-x\right)+6x+4\left(-x\right)+12$$

Combine x and 6x to get 7x.

$$7x+4+2x\left(-x\right)+4\left(-x\right)+12$$

Add 4 and 12 to get 16.

$$7x+16+2x\left(-x\right)+4\left(-x\right)$$

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

$$7x+16+2x^{2}\left(-1\right)+4\left(-1\right)x$$

Multiply 2 and -1 to get -2.

$$7x+16-2x^{2}+4\left(-1\right)x$$

Multiply 4 and -1 to get -4.

$$7x+16-2x^{2}-4x$$

Combine 7x and -4x to get 3x.

$$3x+16-2x^{2}$$

Expand

$$16+3x-2x^{2}$$

Solution Steps

The opposite of -2 is 2.

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

The opposite of -3 is 3.

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

Use the distributive property to multiply 2 by x+2.

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

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

$$x+4+2x\left(-x\right)+6x+4\left(-x\right)+12$$

Combine x and 6x to get 7x.

$$7x+4+2x\left(-x\right)+4\left(-x\right)+12$$

Add 4 and 12 to get 16.

$$7x+16+2x\left(-x\right)+4\left(-x\right)$$

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

$$7x+16+2x^{2}\left(-1\right)+4\left(-1\right)x$$

Multiply 2 and -1 to get -2.

$$7x+16-2x^{2}+4\left(-1\right)x$$

Multiply 4 and -1 to get -4.

$$7x+16-2x^{2}-4x$$

Combine 7x and -4x to get 3x.

$$3x+16-2x^{2}$$