Solve 30(50-2x)(40-2x)+20*(2000-50-2x)(40-2x)

$$30 ( 50 - 2 x ) ( 40 - 2 x ) + 20 \times ( 2000 - 50 - 2 x ) ( 40 - 2 x )$$

Evaluate

$$200\left(x-405\right)\left(x-20\right)$$

Solution Steps

Use the distributive property to multiply 30 by 50-2x.

$$\left(1500-60x\right)\left(40-2x\right)+20\left(2000-50-2x\right)\left(40-2x\right)$$

Apply the distributive property by multiplying each term of 1500-60x by each term of 40-2x.

$$60000-3000x-2400x+120x^{2}+20\left(2000-50-2x\right)\left(40-2x\right)$$

Combine -3000x and -2400x to get -5400x.

$$60000-5400x+120x^{2}+20\left(2000-50-2x\right)\left(40-2x\right)$$

Subtract 50 from 2000 to get 1950.

$$60000-5400x+120x^{2}+20\left(1950-2x\right)\left(40-2x\right)$$

Use the distributive property to multiply 20 by 1950-2x.

$$60000-5400x+120x^{2}+\left(39000-40x\right)\left(40-2x\right)$$

Apply the distributive property by multiplying each term of 39000-40x by each term of 40-2x.

$$60000-5400x+120x^{2}[phone]x-1600x+80x^{2}$$

Combine -78000x and -1600x to get -79600x.

$$60000-5400x+120x^{2}[phone]x+80x^{2}$$

Add 60000 and 1560000 to get 1620000.

$$1620000-5400x+120x^{2}-79600x+80x^{2}$$

Combine -5400x and -79600x to get -85000x.

$$1620000-85000x+120x^{2}+80x^{2}$$

Combine 120x^{2} and 80x^{2} to get 200x^{2}.

$$1620000-85000x+200x^{2}$$

Expand

$$200x^{2}-85000x+1620000$$

Solution Steps

Use the distributive property to multiply 30 by 50-2x.

$$\left(1500-60x\right)\left(40-2x\right)+20\left(2000-50-2x\right)\left(40-2x\right)$$

Apply the distributive property by multiplying each term of 1500-60x by each term of 40-2x.

$$60000-3000x-2400x+120x^{2}+20\left(2000-50-2x\right)\left(40-2x\right)$$

Combine -3000x and -2400x to get -5400x.

$$60000-5400x+120x^{2}+20\left(2000-50-2x\right)\left(40-2x\right)$$

Subtract 50 from 2000 to get 1950.

$$60000-5400x+120x^{2}+20\left(1950-2x\right)\left(40-2x\right)$$

Use the distributive property to multiply 20 by 1950-2x.

$$60000-5400x+120x^{2}+\left(39000-40x\right)\left(40-2x\right)$$

Apply the distributive property by multiplying each term of 39000-40x by each term of 40-2x.

$$60000-5400x+120x^{2}[phone]x-1600x+80x^{2}$$

Combine -78000x and -1600x to get -79600x.

$$60000-5400x+120x^{2}[phone]x+80x^{2}$$

Add 60000 and 1560000 to get 1620000.

$$1620000-5400x+120x^{2}-79600x+80x^{2}$$

Combine -5400x and -79600x to get -85000x.

$$1620000-85000x+120x^{2}+80x^{2}$$

Combine 120x^{2} and 80x^{2} to get 200x^{2}.

$$1620000-85000x+200x^{2}$$