Solve (-7/2x+44)(-x+75)-80x

$$( - \frac { 7 } { 2 } x + 44 ) ( - x + 75 ) - 80 x$$

Evaluate

$$\frac{7x^{2}}{2}-\frac{773x}{2}+3300$$

Solution Steps

Apply the distributive property by multiplying each term of -\frac{7}{2}x+44 by each term of -x+75.

$$-\frac{7}{2}x\left(-x\right)-\frac{7}{2}x\times 75+44\left(-x\right)+3300-80x$$

Multiply -\frac{7}{2} and -1 to get \frac{7}{2}.

$$\frac{7}{2}xx-\frac{7}{2}x\times 75+44\left(-x\right)+3300-80x$$

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

$$\frac{7}{2}x^{2}-\frac{7}{2}x\times 75+44\left(-x\right)+3300-80x$$

Express -\frac{7}{2}\times 75 as a single fraction.

$$\frac{7}{2}x^{2}+\frac{-7\times 75}{2}x+44\left(-x\right)+3300-80x$$

Multiply -7 and 75 to get -525.

$$\frac{7}{2}x^{2}+\frac{-525}{2}x+44\left(-x\right)+3300-80x$$

Fraction \frac{-525}{2} can be rewritten as -\frac{525}{2} by extracting the negative sign.

$$\frac{7}{2}x^{2}-\frac{525}{2}x+44\left(-x\right)+3300-80x$$

Combine -\frac{525}{2}x and -80x to get -\frac{685}{2}x.

$$\frac{7}{2}x^{2}-\frac{685}{2}x+44\left(-x\right)+3300$$

Multiply 44 and -1 to get -44.

$$\frac{7}{2}x^{2}-\frac{685}{2}x-44x+3300$$

Combine -\frac{685}{2}x and -44x to get -\frac{773}{2}x.

$$\frac{7}{2}x^{2}-\frac{773}{2}x+3300$$

Expand

$$\frac{7x^{2}}{2}-\frac{773x}{2}+3300$$

Solution Steps

Apply the distributive property by multiplying each term of -\frac{7}{2}x+44 by each term of -x+75.

$$-\frac{7}{2}x\left(-x\right)-\frac{7}{2}x\times 75+44\left(-x\right)+3300-80x$$

Multiply -\frac{7}{2} and -1 to get \frac{7}{2}.

$$\frac{7}{2}xx-\frac{7}{2}x\times 75+44\left(-x\right)+3300-80x$$

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

$$\frac{7}{2}x^{2}-\frac{7}{2}x\times 75+44\left(-x\right)+3300-80x$$

Express -\frac{7}{2}\times 75 as a single fraction.

$$\frac{7}{2}x^{2}+\frac{-7\times 75}{2}x+44\left(-x\right)+3300-80x$$

Multiply -7 and 75 to get -525.

$$\frac{7}{2}x^{2}+\frac{-525}{2}x+44\left(-x\right)+3300-80x$$

Fraction \frac{-525}{2} can be rewritten as -\frac{525}{2} by extracting the negative sign.

$$\frac{7}{2}x^{2}-\frac{525}{2}x+44\left(-x\right)+3300-80x$$

Combine -\frac{525}{2}x and -80x to get -\frac{685}{2}x.

$$\frac{7}{2}x^{2}-\frac{685}{2}x+44\left(-x\right)+3300$$

Multiply 44 and -1 to get -44.

$$\frac{7}{2}x^{2}-\frac{685}{2}x-44x+3300$$

Combine -\frac{685}{2}x and -44x to get -\frac{773}{2}x.

$$\frac{7}{2}x^{2}-\frac{773}{2}x+3300$$