Solve (8x+7)(-3x-4)-(8x+7)(4x-9)

$$( 8 x + 7 ) ( - 3 x - 4 ) - ( 8 x + 7 ) ( 4 x - 9 )$$

Evaluate

$$\left(5-7x\right)\left(8x+7\right)$$

Solution Steps

Apply the distributive property by multiplying each term of 8x+7 by each term of -3x-4.

$$-24x^{2}-32x-21x-28-\left(8x+7\right)\left(4x-9\right)$$

Combine -32x and -21x to get -53x.

$$-24x^{2}-53x-28-\left(8x+7\right)\left(4x-9\right)$$

Apply the distributive property by multiplying each term of 8x+7 by each term of 4x-9.

$$-24x^{2}-53x-28-\left(32x^{2}-72x+28x-63\right)$$

Combine -72x and 28x to get -44x.

$$-24x^{2}-53x-28-\left(32x^{2}-44x-63\right)$$

To find the opposite of 32x^{2}-44x-63, find the opposite of each term.

$$-24x^{2}-53x-28-32x^{2}-\left(-44x\right)-\left(-63\right)$$

The opposite of -44x is 44x.

$$-24x^{2}-53x-28-32x^{2}+44x-\left(-63\right)$$

The opposite of -63 is 63.

$$-24x^{2}-53x-28-32x^{2}+44x+63$$

Combine -24x^{2} and -32x^{2} to get -56x^{2}.

$$-56x^{2}-53x-28+44x+63$$

Combine -53x and 44x to get -9x.

$$-56x^{2}-9x-28+63$$

Add -28 and 63 to get 35.

$$-56x^{2}-9x+35$$

Expand

$$35-9x-56x^{2}$$

Solution Steps

Apply the distributive property by multiplying each term of 8x+7 by each term of -3x-4.

$$-24x^{2}-32x-21x-28-\left(8x+7\right)\left(4x-9\right)$$

Combine -32x and -21x to get -53x.

$$-24x^{2}-53x-28-\left(8x+7\right)\left(4x-9\right)$$

Apply the distributive property by multiplying each term of 8x+7 by each term of 4x-9.

$$-24x^{2}-53x-28-\left(32x^{2}-72x+28x-63\right)$$

Combine -72x and 28x to get -44x.

$$-24x^{2}-53x-28-\left(32x^{2}-44x-63\right)$$

To find the opposite of 32x^{2}-44x-63, find the opposite of each term.

$$-24x^{2}-53x-28-32x^{2}-\left(-44x\right)-\left(-63\right)$$

The opposite of -44x is 44x.

$$-24x^{2}-53x-28-32x^{2}+44x-\left(-63\right)$$

The opposite of -63 is 63.

$$-24x^{2}-53x-28-32x^{2}+44x+63$$

Combine -24x^{2} and -32x^{2} to get -56x^{2}.

$$-56x^{2}-53x-28+44x+63$$

Combine -53x and 44x to get -9x.

$$-56x^{2}-9x-28+63$$

Add -28 and 63 to get 35.

$$-56x^{2}-9x+35$$