Solve (10x+8)(4x-8)-(5x+7)(6x-9)/4=

$$\frac { ( 10 x + 8 ) ( 4 x - 8 ) - ( 5 x + 7 ) ( 6 x - 9 ) } { 4 } =$$

Evaluate

$$\frac{5x^{2}}{2}-\frac{45x}{4}-\frac{1}{4}$$

Solution Steps

Apply the distributive property by multiplying each term of 10x+8 by each term of 4x-8.

$$\frac{40x^{2}-80x+32x-64-\left(5x+7\right)\left(6x-9\right)}{4}$$

Combine -80x and 32x to get -48x.

$$\frac{40x^{2}-48x-64-\left(5x+7\right)\left(6x-9\right)}{4}$$

Apply the distributive property by multiplying each term of 5x+7 by each term of 6x-9.

$$\frac{40x^{2}-48x-64-\left(30x^{2}-45x+42x-63\right)}{4}$$

Combine -45x and 42x to get -3x.

$$\frac{40x^{2}-48x-64-\left(30x^{2}-3x-63\right)}{4}$$

To find the opposite of 30x^{2}-3x-63, find the opposite of each term.

$$\frac{40x^{2}-48x-64-30x^{2}-\left(-3x\right)-\left(-63\right)}{4}$$

The opposite of -3x is 3x.

$$\frac{40x^{2}-48x-64-30x^{2}+3x-\left(-63\right)}{4}$$

The opposite of -63 is 63.

$$\frac{40x^{2}-48x-64-30x^{2}+3x+63}{4}$$

Combine 40x^{2} and -30x^{2} to get 10x^{2}.

$$\frac{10x^{2}-48x-64+3x+63}{4}$$

Combine -48x and 3x to get -45x.

$$\frac{10x^{2}-45x-64+63}{4}$$

Add -64 and 63 to get -1.

$$\frac{10x^{2}-45x-1}{4}$$

Expand

$$\frac{5x^{2}}{2}-\frac{45x}{4}-\frac{1}{4}$$

Solution Steps

Apply the distributive property by multiplying each term of 10x+8 by each term of 4x-8.

$$\frac{40x^{2}-80x+32x-64-\left(5x+7\right)\left(6x-9\right)}{4}$$

Combine -80x and 32x to get -48x.

$$\frac{40x^{2}-48x-64-\left(5x+7\right)\left(6x-9\right)}{4}$$

Apply the distributive property by multiplying each term of 5x+7 by each term of 6x-9.

$$\frac{40x^{2}-48x-64-\left(30x^{2}-45x+42x-63\right)}{4}$$

Combine -45x and 42x to get -3x.

$$\frac{40x^{2}-48x-64-\left(30x^{2}-3x-63\right)}{4}$$

To find the opposite of 30x^{2}-3x-63, find the opposite of each term.

$$\frac{40x^{2}-48x-64-30x^{2}-\left(-3x\right)-\left(-63\right)}{4}$$

The opposite of -3x is 3x.

$$\frac{40x^{2}-48x-64-30x^{2}+3x-\left(-63\right)}{4}$$

The opposite of -63 is 63.

$$\frac{40x^{2}-48x-64-30x^{2}+3x+63}{4}$$

Combine 40x^{2} and -30x^{2} to get 10x^{2}.

$$\frac{10x^{2}-48x-64+3x+63}{4}$$

Combine -48x and 3x to get -45x.

$$\frac{10x^{2}-45x-64+63}{4}$$

Add -64 and 63 to get -1.

$$\frac{10x^{2}-45x-1}{4}$$