Solve f(x)=-2/3(x+1)(x-5)

$$f ( x ) = - \frac { 2 } { 3 } ( x + 1 ) ( x - 5 )$$

Evaluate

$$-\frac{2\left(x-5\right)\left(x+1\right)}{3}$$

Solution Steps

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

$$\left(-\frac{2}{3}x-\frac{2}{3}\right)\left(x-5\right)$$

Apply the distributive property by multiplying each term of -\frac{2}{3}x-\frac{2}{3} by each term of x-5.

$$-\frac{2}{3}xx-\frac{2}{3}x\left(-5\right)-\frac{2}{3}x-\frac{2}{3}\left(-5\right)$$

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

$$-\frac{2}{3}x^{2}-\frac{2}{3}x\left(-5\right)-\frac{2}{3}x-\frac{2}{3}\left(-5\right)$$

Express -\frac{2}{3}\left(-5\right) as a single fraction.

$$-\frac{2}{3}x^{2}+\frac{-2\left(-5\right)}{3}x-\frac{2}{3}x-\frac{2}{3}\left(-5\right)$$

Multiply -2 and -5 to get 10.

$$-\frac{2}{3}x^{2}+\frac{10}{3}x-\frac{2}{3}x-\frac{2}{3}\left(-5\right)$$

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

$$-\frac{2}{3}x^{2}+\frac{8}{3}x-\frac{2}{3}\left(-5\right)$$

Express -\frac{2}{3}\left(-5\right) as a single fraction.

$$-\frac{2}{3}x^{2}+\frac{8}{3}x+\frac{-2\left(-5\right)}{3}$$

Multiply -2 and -5 to get 10.

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

Expand

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

Solution Steps

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

$$\left(-\frac{2}{3}x-\frac{2}{3}\right)\left(x-5\right)$$

Apply the distributive property by multiplying each term of -\frac{2}{3}x-\frac{2}{3} by each term of x-5.

$$-\frac{2}{3}xx-\frac{2}{3}x\left(-5\right)-\frac{2}{3}x-\frac{2}{3}\left(-5\right)$$

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

$$-\frac{2}{3}x^{2}-\frac{2}{3}x\left(-5\right)-\frac{2}{3}x-\frac{2}{3}\left(-5\right)$$

Express -\frac{2}{3}\left(-5\right) as a single fraction.

$$-\frac{2}{3}x^{2}+\frac{-2\left(-5\right)}{3}x-\frac{2}{3}x-\frac{2}{3}\left(-5\right)$$

Multiply -2 and -5 to get 10.

$$-\frac{2}{3}x^{2}+\frac{10}{3}x-\frac{2}{3}x-\frac{2}{3}\left(-5\right)$$

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

$$-\frac{2}{3}x^{2}+\frac{8}{3}x-\frac{2}{3}\left(-5\right)$$

Express -\frac{2}{3}\left(-5\right) as a single fraction.

$$-\frac{2}{3}x^{2}+\frac{8}{3}x+\frac{-2\left(-5\right)}{3}$$

Multiply -2 and -5 to get 10.

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