Solve (4x-80)x+(55(20-x)-200)(20-x)

$$( 4 x - 80 ) x + ( 55 ( 20 - x ) - 200 ) ( 20 - x )$$

Evaluate

$$\left(x-20\right)\left(59x-900\right)$$

Solution Steps

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

$$4x^{2}-80x+\left(55\left(20-x\right)-200\right)\left(20-x\right)$$

Use the distributive property to multiply 55 by 20-x.

$$4x^{2}-80x+\left(1100-55x-200\right)\left(20-x\right)$$

Subtract 200 from 1100 to get 900.

$$4x^{2}-80x+\left(900-55x\right)\left(20-x\right)$$

Apply the distributive property by multiplying each term of 900-55x by each term of 20-x.

$$4x^{2}-80x+18000-900x-1100x+55x^{2}$$

Combine -900x and -1100x to get -2000x.

$$4x^{2}-80x+18000-2000x+55x^{2}$$

Combine -80x and -2000x to get -2080x.

$$4x^{2}-2080x+18000+55x^{2}$$

Combine 4x^{2} and 55x^{2} to get 59x^{2}.

$$59x^{2}-2080x+18000$$

Expand

$$59x^{2}-2080x+18000$$

Solution Steps

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

$$4x^{2}-80x+\left(55\left(20-x\right)-200\right)\left(20-x\right)$$

Use the distributive property to multiply 55 by 20-x.

$$4x^{2}-80x+\left(1100-55x-200\right)\left(20-x\right)$$

Subtract 200 from 1100 to get 900.

$$4x^{2}-80x+\left(900-55x\right)\left(20-x\right)$$

Apply the distributive property by multiplying each term of 900-55x by each term of 20-x.

$$4x^{2}-80x+18000-900x-1100x+55x^{2}$$

Combine -900x and -1100x to get -2000x.

$$4x^{2}-80x+18000-2000x+55x^{2}$$

Combine -80x and -2000x to get -2080x.

$$4x^{2}-2080x+18000+55x^{2}$$

Combine 4x^{2} and 55x^{2} to get 59x^{2}.

$$59x^{2}-2080x+18000$$