Solve -1/2(x+2)(x-4)

$$- \frac { 1 } { 2 } ( x + 2 ) ( x - 4 )$$

Evaluate

$$-\frac{\left(x-4\right)\left(x+2\right)}{2}$$

Solution Steps

Use the distributive property to multiply -\frac{1}{2} by x+2.

$$\left(-\frac{1}{2}x-\frac{1}{2}\times 2\right)\left(x-4\right)$$

Cancel out 2 and 2.

$$\left(-\frac{1}{2}x-1\right)\left(x-4\right)$$

Apply the distributive property by multiplying each term of -\frac{1}{2}x-1 by each term of x-4.

$$-\frac{1}{2}xx-\frac{1}{2}x\left(-4\right)-x+4$$

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

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

Express -\frac{1}{2}\left(-4\right) as a single fraction.

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

Multiply -1 and -4 to get 4.

$$-\frac{1}{2}x^{2}+\frac{4}{2}x-x+4$$

Divide 4 by 2 to get 2.

$$-\frac{1}{2}x^{2}+2x-x+4$$

Combine 2x and -x to get x.

$$-\frac{1}{2}x^{2}+x+4$$

Expand

$$-\frac{x^{2}}{2}+x+4$$

Solution Steps

Use the distributive property to multiply -\frac{1}{2} by x+2.

$$\left(-\frac{1}{2}x-\frac{1}{2}\times 2\right)\left(x-4\right)$$

Cancel out 2 and 2.

$$\left(-\frac{1}{2}x-1\right)\left(x-4\right)$$

Apply the distributive property by multiplying each term of -\frac{1}{2}x-1 by each term of x-4.

$$-\frac{1}{2}xx-\frac{1}{2}x\left(-4\right)-x+4$$

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

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

Express -\frac{1}{2}\left(-4\right) as a single fraction.

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

Multiply -1 and -4 to get 4.

$$-\frac{1}{2}x^{2}+\frac{4}{2}x-x+4$$

Divide 4 by 2 to get 2.

$$-\frac{1}{2}x^{2}+2x-x+4$$

Combine 2x and -x to get x.

$$-\frac{1}{2}x^{2}+x+4$$