Solve (-1/2x+1/2)(-500x+750)

$$( - \frac { 1 } { 2 } x + \frac { 1 } { 2 } ) ( - 500 x + 750 )$$

Evaluate

$$125\left(x-1\right)\left(2x-3\right)$$

Solution Steps

Apply the distributive property by multiplying each term of -\frac{1}{2}x+\frac{1}{2} by each term of -500x+750.

$$-\frac{1}{2}x\left(-500\right)x-\frac{1}{2}x\times 750+\frac{1}{2}\left(-500\right)x+\frac{1}{2}\times 750$$

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

$$-\frac{1}{2}x^{2}\left(-500\right)-\frac{1}{2}x\times 750+\frac{1}{2}\left(-500\right)x+\frac{1}{2}\times 750$$

Express -\frac{1}{2}\left(-500\right) as a single fraction.

$$\frac{-\left(-500\right)}{2}x^{2}-\frac{1}{2}x\times 750+\frac{1}{2}\left(-500\right)x+\frac{1}{2}\times 750$$

Multiply -1 and -500 to get 500.

$$\frac{500}{2}x^{2}-\frac{1}{2}x\times 750+\frac{1}{2}\left(-500\right)x+\frac{1}{2}\times 750$$

Divide 500 by 2 to get 250.

$$250x^{2}-\frac{1}{2}x\times 750+\frac{1}{2}\left(-500\right)x+\frac{1}{2}\times 750$$

Express -\frac{1}{2}\times 750 as a single fraction.

$$250x^{2}+\frac{-750}{2}x+\frac{1}{2}\left(-500\right)x+\frac{1}{2}\times 750$$

Divide -750 by 2 to get -375.

$$250x^{2}-375x+\frac{1}{2}\left(-500\right)x+\frac{1}{2}\times 750$$

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

$$250x^{2}-375x+\frac{-500}{2}x+\frac{1}{2}\times 750$$

Divide -500 by 2 to get -250.

$$250x^{2}-375x-250x+\frac{1}{2}\times 750$$

Combine -375x and -250x to get -625x.

$$250x^{2}-625x+\frac{1}{2}\times 750$$

Multiply \frac{1}{2} and 750 to get \frac{750}{2}.

$$250x^{2}-625x+\frac{750}{2}$$

Divide 750 by 2 to get 375.

$$250x^{2}-625x+375$$

Expand

$$250x^{2}-625x+375$$

Solution Steps

Apply the distributive property by multiplying each term of -\frac{1}{2}x+\frac{1}{2} by each term of -500x+750.

$$-\frac{1}{2}x\left(-500\right)x-\frac{1}{2}x\times 750+\frac{1}{2}\left(-500\right)x+\frac{1}{2}\times 750$$

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

$$-\frac{1}{2}x^{2}\left(-500\right)-\frac{1}{2}x\times 750+\frac{1}{2}\left(-500\right)x+\frac{1}{2}\times 750$$

Express -\frac{1}{2}\left(-500\right) as a single fraction.

$$\frac{-\left(-500\right)}{2}x^{2}-\frac{1}{2}x\times 750+\frac{1}{2}\left(-500\right)x+\frac{1}{2}\times 750$$

Multiply -1 and -500 to get 500.

$$\frac{500}{2}x^{2}-\frac{1}{2}x\times 750+\frac{1}{2}\left(-500\right)x+\frac{1}{2}\times 750$$

Divide 500 by 2 to get 250.

$$250x^{2}-\frac{1}{2}x\times 750+\frac{1}{2}\left(-500\right)x+\frac{1}{2}\times 750$$

Express -\frac{1}{2}\times 750 as a single fraction.

$$250x^{2}+\frac{-750}{2}x+\frac{1}{2}\left(-500\right)x+\frac{1}{2}\times 750$$

Divide -750 by 2 to get -375.

$$250x^{2}-375x+\frac{1}{2}\left(-500\right)x+\frac{1}{2}\times 750$$

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

$$250x^{2}-375x+\frac{-500}{2}x+\frac{1}{2}\times 750$$

Divide -500 by 2 to get -250.

$$250x^{2}-375x-250x+\frac{1}{2}\times 750$$

Combine -375x and -250x to get -625x.

$$250x^{2}-625x+\frac{1}{2}\times 750$$

Multiply \frac{1}{2} and 750 to get \frac{750}{2}.

$$250x^{2}-625x+\frac{750}{2}$$

Divide 750 by 2 to get 375.

$$250x^{2}-625x+375$$