Solve g(x)=-1/3(x+2)(x+8)

$$g ( x ) = - \frac { 1 } { 3 } ( x + 2 ) ( x + 8 )$$

Evaluate

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

Solution Steps

Use the distributive property to multiply -\frac{1}{3} by x+2.

$$\left(-\frac{1}{3}x-\frac{1}{3}\times 2\right)\left(x+8\right)$$

Express -\frac{1}{3}\times 2 as a single fraction.

$$\left(-\frac{1}{3}x+\frac{-2}{3}\right)\left(x+8\right)$$

Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

$$\left(-\frac{1}{3}x-\frac{2}{3}\right)\left(x+8\right)$$

Apply the distributive property by multiplying each term of -\frac{1}{3}x-\frac{2}{3} by each term of x+8.

$$-\frac{1}{3}xx-\frac{1}{3}x\times 8-\frac{2}{3}x-\frac{2}{3}\times 8$$

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

$$-\frac{1}{3}x^{2}-\frac{1}{3}x\times 8-\frac{2}{3}x-\frac{2}{3}\times 8$$

Express -\frac{1}{3}\times 8 as a single fraction.

$$-\frac{1}{3}x^{2}+\frac{-8}{3}x-\frac{2}{3}x-\frac{2}{3}\times 8$$

Fraction \frac{-8}{3} can be rewritten as -\frac{8}{3} by extracting the negative sign.

$$-\frac{1}{3}x^{2}-\frac{8}{3}x-\frac{2}{3}x-\frac{2}{3}\times 8$$

Combine -\frac{8}{3}x and -\frac{2}{3}x to get -\frac{10}{3}x.

$$-\frac{1}{3}x^{2}-\frac{10}{3}x-\frac{2}{3}\times 8$$

Express -\frac{2}{3}\times 8 as a single fraction.

$$-\frac{1}{3}x^{2}-\frac{10}{3}x+\frac{-2\times 8}{3}$$

Multiply -2 and 8 to get -16.

$$-\frac{1}{3}x^{2}-\frac{10}{3}x+\frac{-16}{3}$$

Fraction \frac{-16}{3} can be rewritten as -\frac{16}{3} by extracting the negative sign.

$$-\frac{1}{3}x^{2}-\frac{10}{3}x-\frac{16}{3}$$

Expand

$$\frac{-x^{2}-10x-16}{3}$$

Solution Steps

Use the distributive property to multiply -\frac{1}{3} by x+2.

$$\left(-\frac{1}{3}x-\frac{1}{3}\times 2\right)\left(x+8\right)$$

Express -\frac{1}{3}\times 2 as a single fraction.

$$\left(-\frac{1}{3}x+\frac{-2}{3}\right)\left(x+8\right)$$

Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

$$\left(-\frac{1}{3}x-\frac{2}{3}\right)\left(x+8\right)$$

Apply the distributive property by multiplying each term of -\frac{1}{3}x-\frac{2}{3} by each term of x+8.

$$-\frac{1}{3}xx-\frac{1}{3}x\times 8-\frac{2}{3}x-\frac{2}{3}\times 8$$

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

$$-\frac{1}{3}x^{2}-\frac{1}{3}x\times 8-\frac{2}{3}x-\frac{2}{3}\times 8$$

Express -\frac{1}{3}\times 8 as a single fraction.

$$-\frac{1}{3}x^{2}+\frac{-8}{3}x-\frac{2}{3}x-\frac{2}{3}\times 8$$

Fraction \frac{-8}{3} can be rewritten as -\frac{8}{3} by extracting the negative sign.

$$-\frac{1}{3}x^{2}-\frac{8}{3}x-\frac{2}{3}x-\frac{2}{3}\times 8$$

Combine -\frac{8}{3}x and -\frac{2}{3}x to get -\frac{10}{3}x.

$$-\frac{1}{3}x^{2}-\frac{10}{3}x-\frac{2}{3}\times 8$$

Express -\frac{2}{3}\times 8 as a single fraction.

$$-\frac{1}{3}x^{2}-\frac{10}{3}x+\frac{-2\times 8}{3}$$

Multiply -2 and 8 to get -16.

$$-\frac{1}{3}x^{2}-\frac{10}{3}x+\frac{-16}{3}$$

Fraction \frac{-16}{3} can be rewritten as -\frac{16}{3} by extracting the negative sign.

$$-\frac{1}{3}x^{2}-\frac{10}{3}x-\frac{16}{3}$$