Solve (6-x)(20+2x)+(40-2x)(4+x)

$$( 6 - x ) ( 20 + 2 x ) + ( 40 - 2 x ) ( 4 + x )$$

Evaluate

$$280+24x-4x^{2}$$

Solution Steps

Apply the distributive property by multiplying each term of 6-x by each term of 20+2x.

$$120+12x-20x-2x^{2}+\left(40-2x\right)\left(4+x\right)$$

Combine 12x and -20x to get -8x.

$$120-8x-2x^{2}+\left(40-2x\right)\left(4+x\right)$$

Apply the distributive property by multiplying each term of 40-2x by each term of 4+x.

$$120-8x-2x^{2}+160+40x-8x-2x^{2}$$

Combine 40x and -8x to get 32x.

$$120-8x-2x^{2}+160+32x-2x^{2}$$

Add 120 and 160 to get 280.

$$280-8x-2x^{2}+32x-2x^{2}$$

Combine -8x and 32x to get 24x.

$$280+24x-2x^{2}-2x^{2}$$

Combine -2x^{2} and -2x^{2} to get -4x^{2}.

$$280+24x-4x^{2}$$

Expand

$$280+24x-4x^{2}$$

Solution Steps

Apply the distributive property by multiplying each term of 6-x by each term of 20+2x.

$$120+12x-20x-2x^{2}+\left(40-2x\right)\left(4+x\right)$$

Combine 12x and -20x to get -8x.

$$120-8x-2x^{2}+\left(40-2x\right)\left(4+x\right)$$

Apply the distributive property by multiplying each term of 40-2x by each term of 4+x.

$$120-8x-2x^{2}+160+40x-8x-2x^{2}$$

Combine 40x and -8x to get 32x.

$$120-8x-2x^{2}+160+32x-2x^{2}$$

Add 120 and 160 to get 280.

$$280-8x-2x^{2}+32x-2x^{2}$$

Combine -8x and 32x to get 24x.

$$280+24x-2x^{2}-2x^{2}$$

Combine -2x^{2} and -2x^{2} to get -4x^{2}.

$$280+24x-4x^{2}$$