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

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

Evaluate

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

Solution Steps

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

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

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

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

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

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

Divide -500 by 2 to get -250.

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

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

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

Divide -500 by 2 to get -250.

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

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

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

Divide 7500 by 2 to get 3750.

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

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

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

Multiply 7500 and \frac{1}{2} 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 -500x+7500 by each term of \frac{1}{2}x+\frac{1}{2}.

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

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

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

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

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

Divide -500 by 2 to get -250.

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

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

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

Divide -500 by 2 to get -250.

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

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

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

Divide 7500 by 2 to get 3750.

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

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

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

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

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

Divide 7500 by 2 to get 3750.

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