Solve (1/2x+1/2)(-500x+7500)

$$( \frac { 1 } { 2 } x + \frac { 1 } { 2 } ) ( - 500 x + 7500 )$$

Evaluate

$$250\left(15-x\right)\left(x+1\right)$$

Solution Steps

Apply the distributive property by multiplying each term of \frac{1}{2}x+\frac{1}{2} by each term of -500x+7500.

$$\frac{1}{2}x\left(-500\right)x+\frac{1}{2}x\times 7500+\frac{1}{2}\left(-500\right)x+\frac{1}{2}\times 7500$$

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

$$\frac{1}{2}x^{2}\left(-500\right)+\frac{1}{2}x\times 7500+\frac{1}{2}\left(-500\right)x+\frac{1}{2}\times 7500$$

Multiply \frac{1}{2} and -500 to get \frac{-500}{2}.

$$\frac{-500}{2}x^{2}+\frac{1}{2}x\times 7500+\frac{1}{2}\left(-500\right)x+\frac{1}{2}\times 7500$$

Divide -500 by 2 to get -250.

$$-250x^{2}+\frac{1}{2}x\times 7500+\frac{1}{2}\left(-500\right)x+\frac{1}{2}\times 7500$$

Multiply \frac{1}{2} and 7500 to get \frac{7500}{2}.

$$-250x^{2}+\frac{7500}{2}x+\frac{1}{2}\left(-500\right)x+\frac{1}{2}\times 7500$$

Divide 7500 by 2 to get 3750.

$$-250x^{2}+3750x+\frac{1}{2}\left(-500\right)x+\frac{1}{2}\times 7500$$

Multiply \frac{1}{2} and -500 to get \frac{-500}{2}.

$$-250x^{2}+3750x+\frac{-500}{2}x+\frac{1}{2}\times 7500$$

Divide -500 by 2 to get -250.

$$-250x^{2}+3750x-250x+\frac{1}{2}\times 7500$$

Combine 3750x and -250x to get 3500x.

$$-250x^{2}+3500x+\frac{1}{2}\times 7500$$

Multiply \frac{1}{2} and 7500 to get \frac{7500}{2}.

$$-250x^{2}+3500x+\frac{7500}{2}$$

Divide 7500 by 2 to get 3750.

$$-250x^{2}+3500x+3750$$

Expand

$$3750+3500x-250x^{2}$$

Solution Steps

Apply the distributive property by multiplying each term of \frac{1}{2}x+\frac{1}{2} by each term of -500x+7500.

$$\frac{1}{2}x\left(-500\right)x+\frac{1}{2}x\times 7500+\frac{1}{2}\left(-500\right)x+\frac{1}{2}\times 7500$$

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

$$\frac{1}{2}x^{2}\left(-500\right)+\frac{1}{2}x\times 7500+\frac{1}{2}\left(-500\right)x+\frac{1}{2}\times 7500$$

Multiply \frac{1}{2} and -500 to get \frac{-500}{2}.

$$\frac{-500}{2}x^{2}+\frac{1}{2}x\times 7500+\frac{1}{2}\left(-500\right)x+\frac{1}{2}\times 7500$$

Divide -500 by 2 to get -250.

$$-250x^{2}+\frac{1}{2}x\times 7500+\frac{1}{2}\left(-500\right)x+\frac{1}{2}\times 7500$$

Multiply \frac{1}{2} and 7500 to get \frac{7500}{2}.

$$-250x^{2}+\frac{7500}{2}x+\frac{1}{2}\left(-500\right)x+\frac{1}{2}\times 7500$$

Divide 7500 by 2 to get 3750.

$$-250x^{2}+3750x+\frac{1}{2}\left(-500\right)x+\frac{1}{2}\times 7500$$

Multiply \frac{1}{2} and -500 to get \frac{-500}{2}.

$$-250x^{2}+3750x+\frac{-500}{2}x+\frac{1}{2}\times 7500$$

Divide -500 by 2 to get -250.

$$-250x^{2}+3750x-250x+\frac{1}{2}\times 7500$$

Combine 3750x and -250x to get 3500x.

$$-250x^{2}+3500x+\frac{1}{2}\times 7500$$

Multiply \frac{1}{2} and 7500 to get \frac{7500}{2}.

$$-250x^{2}+3500x+\frac{7500}{2}$$

Divide 7500 by 2 to get 3750.

$$-250x^{2}+3500x+3750$$