Solve (x+4)(x+3)-(2x-1)(x-5)

$$( x + 4 ) ( x + 3 ) - ( 2 x - 1 ) ( x - 5 )$$

Evaluate

$$7+18x-x^{2}$$

Solution Steps

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

$$x^{2}+3x+4x+12-\left(2x-1\right)\left(x-5\right)$$

Combine 3x and 4x to get 7x.

$$x^{2}+7x+12-\left(2x-1\right)\left(x-5\right)$$

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

$$x^{2}+7x+12-\left(2x^{2}-10x-x+5\right)$$

Combine -10x and -x to get -11x.

$$x^{2}+7x+12-\left(2x^{2}-11x+5\right)$$

To find the opposite of 2x^{2}-11x+5, find the opposite of each term.

$$x^{2}+7x+12-2x^{2}-\left(-11x\right)-5$$

The opposite of -11x is 11x.

$$x^{2}+7x+12-2x^{2}+11x-5$$

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

$$-x^{2}+7x+12+11x-5$$

Combine 7x and 11x to get 18x.

$$-x^{2}+18x+12-5$$

Subtract 5 from 12 to get 7.

$$-x^{2}+18x+7$$

Expand

$$7+18x-x^{2}$$

Solution Steps

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

$$x^{2}+3x+4x+12-\left(2x-1\right)\left(x-5\right)$$

Combine 3x and 4x to get 7x.

$$x^{2}+7x+12-\left(2x-1\right)\left(x-5\right)$$

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

$$x^{2}+7x+12-\left(2x^{2}-10x-x+5\right)$$

Combine -10x and -x to get -11x.

$$x^{2}+7x+12-\left(2x^{2}-11x+5\right)$$

To find the opposite of 2x^{2}-11x+5, find the opposite of each term.

$$x^{2}+7x+12-2x^{2}-\left(-11x\right)-5$$

The opposite of -11x is 11x.

$$x^{2}+7x+12-2x^{2}+11x-5$$

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

$$-x^{2}+7x+12+11x-5$$

Combine 7x and 11x to get 18x.

$$-x^{2}+18x+12-5$$

Subtract 5 from 12 to get 7.

$$-x^{2}+18x+7$$