Solve (3x+8)(x-4)-(x-4)(x-8)

$$( 3 x + 8 ) ( x - 4 ) - ( x - 4 ) ( x - 8 )$$

Evaluate

$$2\left(x-4\right)\left(x+8\right)$$

Solution Steps

Apply the distributive property by multiplying each term of 3x+8 by each term of x-4.

$$3x^{2}-12x+8x-32-\left(x-4\right)\left(x-8\right)$$

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

$$3x^{2}-4x-32-\left(x-4\right)\left(x-8\right)$$

Apply the distributive property by multiplying each term of x-4 by each term of x-8.

$$3x^{2}-4x-32-\left(x^{2}-8x-4x+32\right)$$

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

$$3x^{2}-4x-32-\left(x^{2}-12x+32\right)$$

To find the opposite of x^{2}-12x+32, find the opposite of each term.

$$3x^{2}-4x-32-x^{2}-\left(-12x\right)-32$$

The opposite of -12x is 12x.

$$3x^{2}-4x-32-x^{2}+12x-32$$

Combine 3x^{2} and -x^{2} to get 2x^{2}.

$$2x^{2}-4x-32+12x-32$$

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

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

Subtract 32 from -32 to get -64.

$$2x^{2}+8x-64$$

Expand

$$2x^{2}+8x-64$$

Solution Steps

Apply the distributive property by multiplying each term of 3x+8 by each term of x-4.

$$3x^{2}-12x+8x-32-\left(x-4\right)\left(x-8\right)$$

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

$$3x^{2}-4x-32-\left(x-4\right)\left(x-8\right)$$

Apply the distributive property by multiplying each term of x-4 by each term of x-8.

$$3x^{2}-4x-32-\left(x^{2}-8x-4x+32\right)$$

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

$$3x^{2}-4x-32-\left(x^{2}-12x+32\right)$$

To find the opposite of x^{2}-12x+32, find the opposite of each term.

$$3x^{2}-4x-32-x^{2}-\left(-12x\right)-32$$

The opposite of -12x is 12x.

$$3x^{2}-4x-32-x^{2}+12x-32$$

Combine 3x^{2} and -x^{2} to get 2x^{2}.

$$2x^{2}-4x-32+12x-32$$

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

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

Subtract 32 from -32 to get -64.

$$2x^{2}+8x-64$$