Solve (4x-80)x+(5.5(20-x)-200)(20-x)

$$( 4 x - 80 ) x + ( 5.5 ( 20 - x ) - 200 ) ( 20 - x )$$

Evaluate

$$\frac{\left(x-20\right)\left(19x+180\right)}{2}$$

Solution Steps

Use the distributive property to multiply 4x-80 by x.

$$4x^{2}-80x+\left(5.5\left(20-x\right)-200\right)\left(20-x\right)$$

Use the distributive property to multiply 5.5 by 20-x.

$$4x^{2}-80x+\left(110-5.5x-200\right)\left(20-x\right)$$

Subtract 200 from 110 to get -90.

$$4x^{2}-80x+\left(-90-5.5x\right)\left(20-x\right)$$

Apply the distributive property by multiplying each term of -90-5.5x by each term of 20-x.

$$4x^{2}-80x-1800+90x-110x+5.5x^{2}$$

Combine 90x and -110x to get -20x.

$$4x^{2}-80x-1800-20x+5.5x^{2}$$

Combine -80x and -20x to get -100x.

$$4x^{2}-100x-1800+5.5x^{2}$$

Combine 4x^{2} and 5.5x^{2} to get 9.5x^{2}.

$$9.5x^{2}-100x-1800$$

Expand

$$\frac{19x^{2}}{2}-100x-1800$$

Solution Steps

Use the distributive property to multiply 4x-80 by x.

$$4x^{2}-80x+\left(5.5\left(20-x\right)-200\right)\left(20-x\right)$$

Use the distributive property to multiply 5.5 by 20-x.

$$4x^{2}-80x+\left(110-5.5x-200\right)\left(20-x\right)$$

Subtract 200 from 110 to get -90.

$$4x^{2}-80x+\left(-90-5.5x\right)\left(20-x\right)$$

Apply the distributive property by multiplying each term of -90-5.5x by each term of 20-x.

$$4x^{2}-80x-1800+90x-110x+5.5x^{2}$$

Combine 90x and -110x to get -20x.

$$4x^{2}-80x-1800-20x+5.5x^{2}$$

Combine -80x and -20x to get -100x.

$$4x^{2}-100x-1800+5.5x^{2}$$

Combine 4x^{2} and 5.5x^{2} to get 9.5x^{2}.

$$9.5x^{2}-100x-1800$$