Solve -1/2(x+2)(x-5)

$$- \frac { 1 } { 2 } ( x + 2 ) ( x - 5 )$$

Evaluate

$$-\frac{\left(x-5\right)\left(x+2\right)}{2}$$

Solution Steps

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

$$\left(-\frac{1}{2}x-\frac{1}{2}\times 2\right)\left(x-5\right)$$

Cancel out 2 and 2.

$$\left(-\frac{1}{2}x-1\right)\left(x-5\right)$$

Apply the distributive property by multiplying each term of -\frac{1}{2}x-1 by each term of x-5.

$$-\frac{1}{2}xx-\frac{1}{2}x\left(-5\right)-x+5$$

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

$$-\frac{1}{2}x^{2}-\frac{1}{2}x\left(-5\right)-x+5$$

Express -\frac{1}{2}\left(-5\right) as a single fraction.

$$-\frac{1}{2}x^{2}+\frac{-\left(-5\right)}{2}x-x+5$$

Multiply -1 and -5 to get 5.

$$-\frac{1}{2}x^{2}+\frac{5}{2}x-x+5$$

Combine \frac{5}{2}x and -x to get \frac{3}{2}x.

$$-\frac{1}{2}x^{2}+\frac{3}{2}x+5$$

Expand

$$-\frac{x^{2}}{2}+\frac{3x}{2}+5$$

Solution Steps

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

$$\left(-\frac{1}{2}x-\frac{1}{2}\times 2\right)\left(x-5\right)$$

Cancel out 2 and 2.

$$\left(-\frac{1}{2}x-1\right)\left(x-5\right)$$

Apply the distributive property by multiplying each term of -\frac{1}{2}x-1 by each term of x-5.

$$-\frac{1}{2}xx-\frac{1}{2}x\left(-5\right)-x+5$$

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

$$-\frac{1}{2}x^{2}-\frac{1}{2}x\left(-5\right)-x+5$$

Express -\frac{1}{2}\left(-5\right) as a single fraction.

$$-\frac{1}{2}x^{2}+\frac{-\left(-5\right)}{2}x-x+5$$

Multiply -1 and -5 to get 5.

$$-\frac{1}{2}x^{2}+\frac{5}{2}x-x+5$$

Combine \frac{5}{2}x and -x to get \frac{3}{2}x.

$$-\frac{1}{2}x^{2}+\frac{3}{2}x+5$$