Solve (2d-8)(1/2d-4)-(3d-6)(1/3d+1)

$$( 2 d - 8 ) ( \frac { 1 } { 2 } d - 4 ) - ( 3 d - 6 ) ( \frac { 1 } { 3 } d + 1 )$$

Evaluate

$$38-13d$$

Solution Steps

Apply the distributive property by multiplying each term of 2d-8 by each term of \frac{1}{2}d-4.

$$2d\times \frac{1}{2}d-8d-8\times \frac{1}{2}d+32-\left(3d-6\right)\left(\frac{1}{3}d+1\right)$$

Multiply d and d to get d^{2}.

$$2d^{2}\times \frac{1}{2}-8d-8\times \frac{1}{2}d+32-\left(3d-6\right)\left(\frac{1}{3}d+1\right)$$

Cancel out 2 and 2.

$$d^{2}-8d-8\times \frac{1}{2}d+32-\left(3d-6\right)\left(\frac{1}{3}d+1\right)$$

Multiply -8 and \frac{1}{2} to get \frac{-8}{2}.

$$d^{2}-8d+\frac{-8}{2}d+32-\left(3d-6\right)\left(\frac{1}{3}d+1\right)$$

Divide -8 by 2 to get -4.

$$d^{2}-8d-4d+32-\left(3d-6\right)\left(\frac{1}{3}d+1\right)$$

Combine -8d and -4d to get -12d.

$$d^{2}-12d+32-\left(3d-6\right)\left(\frac{1}{3}d+1\right)$$

Apply the distributive property by multiplying each term of 3d-6 by each term of \frac{1}{3}d+1.

$$d^{2}-12d+32-\left(3d\times \frac{1}{3}d+3d-6\times \frac{1}{3}d-6\right)$$

Multiply d and d to get d^{2}.

$$d^{2}-12d+32-\left(3d^{2}\times \frac{1}{3}+3d-6\times \frac{1}{3}d-6\right)$$

Cancel out 3 and 3.

$$d^{2}-12d+32-\left(d^{2}+3d-6\times \frac{1}{3}d-6\right)$$

Multiply -6 and \frac{1}{3} to get \frac{-6}{3}.

$$d^{2}-12d+32-\left(d^{2}+3d+\frac{-6}{3}d-6\right)$$

Divide -6 by 3 to get -2.

$$d^{2}-12d+32-\left(d^{2}+3d-2d-6\right)$$

Combine 3d and -2d to get d.

$$d^{2}-12d+32-\left(d^{2}+d-6\right)$$

To find the opposite of d^{2}+d-6, find the opposite of each term.

$$d^{2}-12d+32-d^{2}-d-\left(-6\right)$$

The opposite of -6 is 6.

$$d^{2}-12d+32-d^{2}-d+6$$

Combine d^{2} and -d^{2} to get 0.

$$-12d+32-d+6$$

Combine -12d and -d to get -13d.

$$-13d+32+6$$

Add 32 and 6 to get 38.

$$-13d+38$$

Expand

$$38-13d$$

Solution Steps

Apply the distributive property by multiplying each term of 2d-8 by each term of \frac{1}{2}d-4.

$$2d\times \frac{1}{2}d-8d-8\times \frac{1}{2}d+32-\left(3d-6\right)\left(\frac{1}{3}d+1\right)$$

Multiply d and d to get d^{2}.

$$2d^{2}\times \frac{1}{2}-8d-8\times \frac{1}{2}d+32-\left(3d-6\right)\left(\frac{1}{3}d+1\right)$$

Cancel out 2 and 2.

$$d^{2}-8d-8\times \frac{1}{2}d+32-\left(3d-6\right)\left(\frac{1}{3}d+1\right)$$

Multiply -8 and \frac{1}{2} to get \frac{-8}{2}.

$$d^{2}-8d+\frac{-8}{2}d+32-\left(3d-6\right)\left(\frac{1}{3}d+1\right)$$

Divide -8 by 2 to get -4.

$$d^{2}-8d-4d+32-\left(3d-6\right)\left(\frac{1}{3}d+1\right)$$

Combine -8d and -4d to get -12d.

$$d^{2}-12d+32-\left(3d-6\right)\left(\frac{1}{3}d+1\right)$$

Apply the distributive property by multiplying each term of 3d-6 by each term of \frac{1}{3}d+1.

$$d^{2}-12d+32-\left(3d\times \frac{1}{3}d+3d-6\times \frac{1}{3}d-6\right)$$

Multiply d and d to get d^{2}.

$$d^{2}-12d+32-\left(3d^{2}\times \frac{1}{3}+3d-6\times \frac{1}{3}d-6\right)$$

Cancel out 3 and 3.

$$d^{2}-12d+32-\left(d^{2}+3d-6\times \frac{1}{3}d-6\right)$$

Multiply -6 and \frac{1}{3} to get \frac{-6}{3}.

$$d^{2}-12d+32-\left(d^{2}+3d+\frac{-6}{3}d-6\right)$$

Divide -6 by 3 to get -2.

$$d^{2}-12d+32-\left(d^{2}+3d-2d-6\right)$$

Combine 3d and -2d to get d.

$$d^{2}-12d+32-\left(d^{2}+d-6\right)$$

To find the opposite of d^{2}+d-6, find the opposite of each term.

$$d^{2}-12d+32-d^{2}-d-\left(-6\right)$$

The opposite of -6 is 6.

$$d^{2}-12d+32-d^{2}-d+6$$

Combine d^{2} and -d^{2} to get 0.

$$-12d+32-d+6$$

Combine -12d and -d to get -13d.

$$-13d+32+6$$

Add 32 and 6 to get 38.

$$-13d+38$$