Solve (4x-5)(x+4)-(4x-5)(4x-3)

$$( 4 x - 5 ) ( x + 4 ) - ( 4 x - 5 ) ( 4 x - 3 )$$

Evaluate

$$\left(7-3x\right)\left(4x-5\right)$$

Solution Steps

Apply the distributive property by multiplying each term of 4x-5 by each term of x+4.

$$4x^{2}+16x-5x-20-\left(4x-5\right)\left(4x-3\right)$$

Combine 16x and -5x to get 11x.

$$4x^{2}+11x-20-\left(4x-5\right)\left(4x-3\right)$$

Apply the distributive property by multiplying each term of 4x-5 by each term of 4x-3.

$$4x^{2}+11x-20-\left(16x^{2}-12x-20x+15\right)$$

Combine -12x and -20x to get -32x.

$$4x^{2}+11x-20-\left(16x^{2}-32x+15\right)$$

To find the opposite of 16x^{2}-32x+15, find the opposite of each term.

$$4x^{2}+11x-20-16x^{2}-\left(-32x\right)-15$$

The opposite of -32x is 32x.

$$4x^{2}+11x-20-16x^{2}+32x-15$$

Combine 4x^{2} and -16x^{2} to get -12x^{2}.

$$-12x^{2}+11x-20+32x-15$$

Combine 11x and 32x to get 43x.

$$-12x^{2}+43x-20-15$$

Subtract 15 from -20 to get -35.

$$-12x^{2}+43x-35$$

Expand

$$-12x^{2}+43x-35$$

Solution Steps

Apply the distributive property by multiplying each term of 4x-5 by each term of x+4.

$$4x^{2}+16x-5x-20-\left(4x-5\right)\left(4x-3\right)$$

Combine 16x and -5x to get 11x.

$$4x^{2}+11x-20-\left(4x-5\right)\left(4x-3\right)$$

Apply the distributive property by multiplying each term of 4x-5 by each term of 4x-3.

$$4x^{2}+11x-20-\left(16x^{2}-12x-20x+15\right)$$

Combine -12x and -20x to get -32x.

$$4x^{2}+11x-20-\left(16x^{2}-32x+15\right)$$

To find the opposite of 16x^{2}-32x+15, find the opposite of each term.

$$4x^{2}+11x-20-16x^{2}-\left(-32x\right)-15$$

The opposite of -32x is 32x.

$$4x^{2}+11x-20-16x^{2}+32x-15$$

Combine 4x^{2} and -16x^{2} to get -12x^{2}.

$$-12x^{2}+11x-20+32x-15$$

Combine 11x and 32x to get 43x.

$$-12x^{2}+43x-20-15$$

Subtract 15 from -20 to get -35.

$$-12x^{2}+43x-35$$