Solve g(x)=-1/2(x+8)(x-6)

$$g ( x ) = - \frac { 1 } { 2 } ( x + 8 ) ( x - 6 )$$

Evaluate

$$-\frac{\left(x-6\right)\left(x+8\right)}{2}$$

Solution Steps

Use the distributive property to multiply -\frac{1}{2} by x+8.

$$\left(-\frac{1}{2}x-\frac{1}{2}\times 8\right)\left(x-6\right)$$

Express -\frac{1}{2}\times 8 as a single fraction.

$$\left(-\frac{1}{2}x+\frac{-8}{2}\right)\left(x-6\right)$$

Divide -8 by 2 to get -4.

$$\left(-\frac{1}{2}x-4\right)\left(x-6\right)$$

Apply the distributive property by multiplying each term of -\frac{1}{2}x-4 by each term of x-6.

$$-\frac{1}{2}xx-\frac{1}{2}x\left(-6\right)-4x+24$$

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

$$-\frac{1}{2}x^{2}-\frac{1}{2}x\left(-6\right)-4x+24$$

Express -\frac{1}{2}\left(-6\right) as a single fraction.

$$-\frac{1}{2}x^{2}+\frac{-\left(-6\right)}{2}x-4x+24$$

Multiply -1 and -6 to get 6.

$$-\frac{1}{2}x^{2}+\frac{6}{2}x-4x+24$$

Divide 6 by 2 to get 3.

$$-\frac{1}{2}x^{2}+3x-4x+24$$

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

$$-\frac{1}{2}x^{2}-x+24$$

Expand

$$-\frac{x^{2}}{2}-x+24$$

Solution Steps

Use the distributive property to multiply -\frac{1}{2} by x+8.

$$\left(-\frac{1}{2}x-\frac{1}{2}\times 8\right)\left(x-6\right)$$

Express -\frac{1}{2}\times 8 as a single fraction.

$$\left(-\frac{1}{2}x+\frac{-8}{2}\right)\left(x-6\right)$$

Divide -8 by 2 to get -4.

$$\left(-\frac{1}{2}x-4\right)\left(x-6\right)$$

Apply the distributive property by multiplying each term of -\frac{1}{2}x-4 by each term of x-6.

$$-\frac{1}{2}xx-\frac{1}{2}x\left(-6\right)-4x+24$$

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

$$-\frac{1}{2}x^{2}-\frac{1}{2}x\left(-6\right)-4x+24$$

Express -\frac{1}{2}\left(-6\right) as a single fraction.

$$-\frac{1}{2}x^{2}+\frac{-\left(-6\right)}{2}x-4x+24$$

Multiply -1 and -6 to get 6.

$$-\frac{1}{2}x^{2}+\frac{6}{2}x-4x+24$$

Divide 6 by 2 to get 3.

$$-\frac{1}{2}x^{2}+3x-4x+24$$

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

$$-\frac{1}{2}x^{2}-x+24$$