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

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

Evaluate

$$-\left(x+5\right)\left(3x+8\right)$$

Solution Steps

Apply the distributive property by multiplying each term of x+5 by each term of 2x-1.

$$2x^{2}-x+10x-5-\left(5x+7\right)\left(x+5\right)$$

Combine -x and 10x to get 9x.

$$2x^{2}+9x-5-\left(5x+7\right)\left(x+5\right)$$

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

$$2x^{2}+9x-5-\left(5x^{2}+25x+7x+35\right)$$

Combine 25x and 7x to get 32x.

$$2x^{2}+9x-5-\left(5x^{2}+32x+35\right)$$

To find the opposite of 5x^{2}+32x+35, find the opposite of each term.

$$2x^{2}+9x-5-5x^{2}-32x-35$$

Combine 2x^{2} and -5x^{2} to get -3x^{2}.

$$-3x^{2}+9x-5-32x-35$$

Combine 9x and -32x to get -23x.

$$-3x^{2}-23x-5-35$$

Subtract 35 from -5 to get -40.

$$-3x^{2}-23x-40$$

Expand

$$-3x^{2}-23x-40$$

Solution Steps

Apply the distributive property by multiplying each term of x+5 by each term of 2x-1.

$$2x^{2}-x+10x-5-\left(5x+7\right)\left(x+5\right)$$

Combine -x and 10x to get 9x.

$$2x^{2}+9x-5-\left(5x+7\right)\left(x+5\right)$$

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

$$2x^{2}+9x-5-\left(5x^{2}+25x+7x+35\right)$$

Combine 25x and 7x to get 32x.

$$2x^{2}+9x-5-\left(5x^{2}+32x+35\right)$$

To find the opposite of 5x^{2}+32x+35, find the opposite of each term.

$$2x^{2}+9x-5-5x^{2}-32x-35$$

Combine 2x^{2} and -5x^{2} to get -3x^{2}.

$$-3x^{2}+9x-5-32x-35$$

Combine 9x and -32x to get -23x.

$$-3x^{2}-23x-5-35$$

Subtract 35 from -5 to get -40.

$$-3x^{2}-23x-40$$