Solve (2x-4)(4x-1)-(x+5)(x+7)

$$( 2 x - 4 ) ( 4 x - 1 ) - ( x + 5 ) ( x + 7 )$$

Evaluate

$$7x^{2}-30x-31$$

Solution Steps

Apply the distributive property by multiplying each term of 2x-4 by each term of 4x-1.

$$8x^{2}-2x-16x+4-\left(x+5\right)\left(x+7\right)$$

Combine -2x and -16x to get -18x.

$$8x^{2}-18x+4-\left(x+5\right)\left(x+7\right)$$

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

$$8x^{2}-18x+4-\left(x^{2}+7x+5x+35\right)$$

Combine 7x and 5x to get 12x.

$$8x^{2}-18x+4-\left(x^{2}+12x+35\right)$$

To find the opposite of x^{2}+12x+35, find the opposite of each term.

$$8x^{2}-18x+4-x^{2}-12x-35$$

Combine 8x^{2} and -x^{2} to get 7x^{2}.

$$7x^{2}-18x+4-12x-35$$

Combine -18x and -12x to get -30x.

$$7x^{2}-30x+4-35$$

Subtract 35 from 4 to get -31.

$$7x^{2}-30x-31$$

Expand

$$7x^{2}-30x-31$$

Solution Steps

Apply the distributive property by multiplying each term of 2x-4 by each term of 4x-1.

$$8x^{2}-2x-16x+4-\left(x+5\right)\left(x+7\right)$$

Combine -2x and -16x to get -18x.

$$8x^{2}-18x+4-\left(x+5\right)\left(x+7\right)$$

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

$$8x^{2}-18x+4-\left(x^{2}+7x+5x+35\right)$$

Combine 7x and 5x to get 12x.

$$8x^{2}-18x+4-\left(x^{2}+12x+35\right)$$

To find the opposite of x^{2}+12x+35, find the opposite of each term.

$$8x^{2}-18x+4-x^{2}-12x-35$$

Combine 8x^{2} and -x^{2} to get 7x^{2}.

$$7x^{2}-18x+4-12x-35$$

Combine -18x and -12x to get -30x.

$$7x^{2}-30x+4-35$$

Subtract 35 from 4 to get -31.

$$7x^{2}-30x-31$$