Solve (2-x)(350-50x)+(1+x)(150-40x)

$$( 2 - x ) ( 350 - 50 x ) + ( 1 + x ) ( 150 - 40 x )$$

Evaluate

$$10\left(x^{2}-34x+85\right)$$

Solution Steps

Apply the distributive property by multiplying each term of 2-x by each term of 350-50x.

$$700-100x-350x+50x^{2}+\left(1+x\right)\left(150-40x\right)$$

Combine -100x and -350x to get -450x.

$$700-450x+50x^{2}+\left(1+x\right)\left(150-40x\right)$$

Apply the distributive property by multiplying each term of 1+x by each term of 150-40x.

$$700-450x+50x^{2}+150-40x+150x-40x^{2}$$

Combine -40x and 150x to get 110x.

$$700-450x+50x^{2}+150+110x-40x^{2}$$

Add 700 and 150 to get 850.

$$850-450x+50x^{2}+110x-40x^{2}$$

Combine -450x and 110x to get -340x.

$$850-340x+50x^{2}-40x^{2}$$

Combine 50x^{2} and -40x^{2} to get 10x^{2}.

$$850-340x+10x^{2}$$

Expand

$$10x^{2}-340x+850$$

Solution Steps

Apply the distributive property by multiplying each term of 2-x by each term of 350-50x.

$$700-100x-350x+50x^{2}+\left(1+x\right)\left(150-40x\right)$$

Combine -100x and -350x to get -450x.

$$700-450x+50x^{2}+\left(1+x\right)\left(150-40x\right)$$

Apply the distributive property by multiplying each term of 1+x by each term of 150-40x.

$$700-450x+50x^{2}+150-40x+150x-40x^{2}$$

Combine -40x and 150x to get 110x.

$$700-450x+50x^{2}+150+110x-40x^{2}$$

Add 700 and 150 to get 850.

$$850-450x+50x^{2}+110x-40x^{2}$$

Combine -450x and 110x to get -340x.

$$850-340x+50x^{2}-40x^{2}$$

Combine 50x^{2} and -40x^{2} to get 10x^{2}.

$$850-340x+10x^{2}$$