Solve (x+3)(x+2)-(2x-1)(x-6)

$$( x + 3 ) ( x + 2 ) - ( 2 x - 1 ) ( x - 6 )$$

Evaluate

$$x\left(18-x\right)$$

Solution Steps

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

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

Combine 2x and 3x to get 5x.

$$x^{2}+5x+6-\left(2x-1\right)\left(x-6\right)$$

Apply the distributive property by multiplying each term of 2x-1 by each term of x-6.

$$x^{2}+5x+6-\left(2x^{2}-12x-x+6\right)$$

Combine -12x and -x to get -13x.

$$x^{2}+5x+6-\left(2x^{2}-13x+6\right)$$

To find the opposite of 2x^{2}-13x+6, find the opposite of each term.

$$x^{2}+5x+6-2x^{2}-\left(-13x\right)-6$$

The opposite of -13x is 13x.

$$x^{2}+5x+6-2x^{2}+13x-6$$

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

$$-x^{2}+5x+6+13x-6$$

Combine 5x and 13x to get 18x.

$$-x^{2}+18x+6-6$$

Subtract 6 from 6 to get 0.

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

Expand

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

Solution Steps

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

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

Combine 2x and 3x to get 5x.

$$x^{2}+5x+6-\left(2x-1\right)\left(x-6\right)$$

Apply the distributive property by multiplying each term of 2x-1 by each term of x-6.

$$x^{2}+5x+6-\left(2x^{2}-12x-x+6\right)$$

Combine -12x and -x to get -13x.

$$x^{2}+5x+6-\left(2x^{2}-13x+6\right)$$

To find the opposite of 2x^{2}-13x+6, find the opposite of each term.

$$x^{2}+5x+6-2x^{2}-\left(-13x\right)-6$$

The opposite of -13x is 13x.

$$x^{2}+5x+6-2x^{2}+13x-6$$

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

$$-x^{2}+5x+6+13x-6$$

Combine 5x and 13x to get 18x.

$$-x^{2}+18x+6-6$$

Subtract 6 from 6 to get 0.

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