Solve 80*200+(80-x)(200+10x)+40(400-10x)-50*800

$$80 \times 200+(80-x)(200+10x)+40(400-10x)-50 \times 800$$

Evaluate

$$-10\left(x-40\right)\left(x+20\right)$$

Solution Steps

Multiply 80 and 200 to get 16000.

$$16000+\left(80-x\right)\left(200+10x\right)+40\left(400-10x\right)-50\times 800$$

Apply the distributive property by multiplying each term of 80-x by each term of 200+10x.

$$16000+16000+800x-200x-10x^{2}+40\left(400-10x\right)-50\times 800$$

Combine 800x and -200x to get 600x.

$$16000+16000+600x-10x^{2}+40\left(400-10x\right)-50\times 800$$

Add 16000 and 16000 to get 32000.

$$32000+600x-10x^{2}+40\left(400-10x\right)-50\times 800$$

Use the distributive property to multiply 40 by 400-10x.

$$32000+600x-10x^{2}[phone]x-50\times 800$$

Add 32000 and 16000 to get 48000.

$$48000+600x-10x^{2}-400x-50\times 800$$

Combine 600x and -400x to get 200x.

$$48000+200x-10x^{2}-50\times 800$$

Multiply 50 and 800 to get 40000.

$$48000+200x-10x^{2}-40000$$

Subtract 40000 from 48000 to get 8000.

$$8000+200x-10x^{2}$$

Expand

$$8000+200x-10x^{2}$$

Solution Steps

Multiply 80 and 200 to get 16000.

$$16000+\left(80-x\right)\left(200+10x\right)+40\left(400-10x\right)-50\times 800$$

Apply the distributive property by multiplying each term of 80-x by each term of 200+10x.

$$16000+16000+800x-200x-10x^{2}+40\left(400-10x\right)-50\times 800$$

Combine 800x and -200x to get 600x.

$$16000+16000+600x-10x^{2}+40\left(400-10x\right)-50\times 800$$

Add 16000 and 16000 to get 32000.

$$32000+600x-10x^{2}+40\left(400-10x\right)-50\times 800$$

Use the distributive property to multiply 40 by 400-10x.

$$32000+600x-10x^{2}[phone]x-50\times 800$$

Add 32000 and 16000 to get 48000.

$$48000+600x-10x^{2}-400x-50\times 800$$

Combine 600x and -400x to get 200x.

$$48000+200x-10x^{2}-50\times 800$$

Multiply 50 and 800 to get 40000.

$$48000+200x-10x^{2}-40000$$

Subtract 40000 from 48000 to get 8000.

$$8000+200x-10x^{2}$$