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

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

Evaluate

$$x^{2}+8x-26$$

Solution Steps

Apply the distributive property by multiplying each term of x-3 by each term of x+2.

$$x^{2}+2x-3x-6-\left(2x+1\right)\left(x-4\right)+2\left(x-3\right)\left(x+4\right)$$

Combine 2x and -3x to get -x.

$$x^{2}-x-6-\left(2x+1\right)\left(x-4\right)+2\left(x-3\right)\left(x+4\right)$$

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

$$x^{2}-x-6-\left(2x^{2}-8x+x-4\right)+2\left(x-3\right)\left(x+4\right)$$

Combine -8x and x to get -7x.

$$x^{2}-x-6-\left(2x^{2}-7x-4\right)+2\left(x-3\right)\left(x+4\right)$$

To find the opposite of 2x^{2}-7x-4, find the opposite of each term.

$$x^{2}-x-6-2x^{2}-\left(-7x\right)-\left(-4\right)+2\left(x-3\right)\left(x+4\right)$$

The opposite of -7x is 7x.

$$x^{2}-x-6-2x^{2}+7x-\left(-4\right)+2\left(x-3\right)\left(x+4\right)$$

The opposite of -4 is 4.

$$x^{2}-x-6-2x^{2}+7x+4+2\left(x-3\right)\left(x+4\right)$$

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

$$-x^{2}-x-6+7x+4+2\left(x-3\right)\left(x+4\right)$$

Combine -x and 7x to get 6x.

$$-x^{2}+6x-6+4+2\left(x-3\right)\left(x+4\right)$$

Add -6 and 4 to get -2.

$$-x^{2}+6x-2+2\left(x-3\right)\left(x+4\right)$$

Use the distributive property to multiply 2 by x-3.

$$-x^{2}+6x-2+\left(2x-6\right)\left(x+4\right)$$

Apply the distributive property by multiplying each term of 2x-6 by each term of x+4.

$$-x^{2}+6x-2+2x^{2}+8x-6x-24$$

Combine 8x and -6x to get 2x.

$$-x^{2}+6x-2+2x^{2}+2x-24$$

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

$$x^{2}+6x-2+2x-24$$

Combine 6x and 2x to get 8x.

$$x^{2}+8x-2-24$$

Subtract 24 from -2 to get -26.

$$x^{2}+8x-26$$

Expand

$$x^{2}+8x-26$$

Solution Steps

Apply the distributive property by multiplying each term of x-3 by each term of x+2.

$$x^{2}+2x-3x-6-\left(2x+1\right)\left(x-4\right)+2\left(x-3\right)\left(x+4\right)$$

Combine 2x and -3x to get -x.

$$x^{2}-x-6-\left(2x+1\right)\left(x-4\right)+2\left(x-3\right)\left(x+4\right)$$

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

$$x^{2}-x-6-\left(2x^{2}-8x+x-4\right)+2\left(x-3\right)\left(x+4\right)$$

Combine -8x and x to get -7x.

$$x^{2}-x-6-\left(2x^{2}-7x-4\right)+2\left(x-3\right)\left(x+4\right)$$

To find the opposite of 2x^{2}-7x-4, find the opposite of each term.

$$x^{2}-x-6-2x^{2}-\left(-7x\right)-\left(-4\right)+2\left(x-3\right)\left(x+4\right)$$

The opposite of -7x is 7x.

$$x^{2}-x-6-2x^{2}+7x-\left(-4\right)+2\left(x-3\right)\left(x+4\right)$$

The opposite of -4 is 4.

$$x^{2}-x-6-2x^{2}+7x+4+2\left(x-3\right)\left(x+4\right)$$

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

$$-x^{2}-x-6+7x+4+2\left(x-3\right)\left(x+4\right)$$

Combine -x and 7x to get 6x.

$$-x^{2}+6x-6+4+2\left(x-3\right)\left(x+4\right)$$

Add -6 and 4 to get -2.

$$-x^{2}+6x-2+2\left(x-3\right)\left(x+4\right)$$

Use the distributive property to multiply 2 by x-3.

$$-x^{2}+6x-2+\left(2x-6\right)\left(x+4\right)$$

Apply the distributive property by multiplying each term of 2x-6 by each term of x+4.

$$-x^{2}+6x-2+2x^{2}+8x-6x-24$$

Combine 8x and -6x to get 2x.

$$-x^{2}+6x-2+2x^{2}+2x-24$$

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

$$x^{2}+6x-2+2x-24$$

Combine 6x and 2x to get 8x.

$$x^{2}+8x-2-24$$

Subtract 24 from -2 to get -26.

$$x^{2}+8x-26$$