Solve (x+4)(x+3)-(2x-1)(x-7)

$$( x + 4 ) ( x + 3 ) - ( 2 x - 1 ) ( x - 7 )$$

Evaluate

$$5+22x-x^{2}$$

Solution Steps

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

$$x^{2}+3x+4x+12-\left(2x-1\right)\left(x-7\right)$$

Combine 3x and 4x to get 7x.

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

Apply the distributive property by multiplying each term of 2x-1 by each term of x-7.

$$x^{2}+7x+12-\left(2x^{2}-14x-x+7\right)$$

Combine -14x and -x to get -15x.

$$x^{2}+7x+12-\left(2x^{2}-15x+7\right)$$

To find the opposite of 2x^{2}-15x+7, find the opposite of each term.

$$x^{2}+7x+12-2x^{2}-\left(-15x\right)-7$$

The opposite of -15x is 15x.

$$x^{2}+7x+12-2x^{2}+15x-7$$

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

$$-x^{2}+7x+12+15x-7$$

Combine 7x and 15x to get 22x.

$$-x^{2}+22x+12-7$$

Subtract 7 from 12 to get 5.

$$-x^{2}+22x+5$$

Expand

$$5+22x-x^{2}$$

Solution Steps

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

$$x^{2}+3x+4x+12-\left(2x-1\right)\left(x-7\right)$$

Combine 3x and 4x to get 7x.

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

Apply the distributive property by multiplying each term of 2x-1 by each term of x-7.

$$x^{2}+7x+12-\left(2x^{2}-14x-x+7\right)$$

Combine -14x and -x to get -15x.

$$x^{2}+7x+12-\left(2x^{2}-15x+7\right)$$

To find the opposite of 2x^{2}-15x+7, find the opposite of each term.

$$x^{2}+7x+12-2x^{2}-\left(-15x\right)-7$$

The opposite of -15x is 15x.

$$x^{2}+7x+12-2x^{2}+15x-7$$

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

$$-x^{2}+7x+12+15x-7$$

Combine 7x and 15x to get 22x.

$$-x^{2}+22x+12-7$$

Subtract 7 from 12 to get 5.

$$-x^{2}+22x+5$$