Solve 800+(200+50x)[10-x-6]+[600-200-(200+50x)]*(-2

$$800 + ( 200 + 50 x ) [ 10 - x - 6 ] + [ 600 - 200 - ( 200 + 50 x ) ] \times ( - 2$$

Evaluate

$$-50\left(x-6\right)\left(x+4\right)$$

Solution Steps

Subtract 6 from 10 to get 4.

$$800+\left(200+50x\right)\left(4-x\right)+\left(600-200-\left(200+50x\right)\right)\left(-2\right)$$

Apply the distributive property by multiplying each term of 200+50x by each term of 4-x.

$$800+800-200x+200x-50x^{2}+\left(600-200-\left(200+50x\right)\right)\left(-2\right)$$

Combine -200x and 200x to get 0.

$$800+800-50x^{2}+\left(600-200-\left(200+50x\right)\right)\left(-2\right)$$

Add 800 and 800 to get 1600.

$$1600-50x^{2}+\left(600-200-\left(200+50x\right)\right)\left(-2\right)$$

Subtract 200 from 600 to get 400.

$$1600-50x^{2}+\left(400-\left(200+50x\right)\right)\left(-2\right)$$

To find the opposite of 200+50x, find the opposite of each term.

$$1600-50x^{2}+\left(400-200-50x\right)\left(-2\right)$$

Subtract 200 from 400 to get 200.

$$1600-50x^{2}+\left(200-50x\right)\left(-2\right)$$

Use the distributive property to multiply 200-50x by -2.

$$1600-50x^{2}-400+100x$$

Subtract 400 from 1600 to get 1200.

$$1200-50x^{2}+100x$$

Expand

$$1200+100x-50x^{2}$$

Solution Steps

Subtract 6 from 10 to get 4.

$$800+\left(200+50x\right)\left(4-x\right)+\left(600-200-\left(200+50x\right)\right)\left(-2\right)$$

Apply the distributive property by multiplying each term of 200+50x by each term of 4-x.

$$800+800-200x+200x-50x^{2}+\left(600-200-\left(200+50x\right)\right)\left(-2\right)$$

Combine -200x and 200x to get 0.

$$800+800-50x^{2}+\left(600-200-\left(200+50x\right)\right)\left(-2\right)$$

Add 800 and 800 to get 1600.

$$1600-50x^{2}+\left(600-200-\left(200+50x\right)\right)\left(-2\right)$$

Subtract 200 from 600 to get 400.

$$1600-50x^{2}+\left(400-\left(200+50x\right)\right)\left(-2\right)$$

To find the opposite of 200+50x, find the opposite of each term.

$$1600-50x^{2}+\left(400-200-50x\right)\left(-2\right)$$

Subtract 200 from 400 to get 200.

$$1600-50x^{2}+\left(200-50x\right)\left(-2\right)$$

Use the distributive property to multiply 200-50x by -2.

$$1600-50x^{2}-400+100x$$

Subtract 400 from 1600 to get 1200.

$$1200-50x^{2}+100x$$