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

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

Evaluate

$$20$$

Solution Steps

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

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

Combine x and 2x to get 3x.

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

Apply the distributive property by multiplying each term of x+6 by each term of x-3.

$$x^{2}+3x+2-\left(x^{2}-3x+6x-18\right)$$

Combine -3x and 6x to get 3x.

$$x^{2}+3x+2-\left(x^{2}+3x-18\right)$$

To find the opposite of x^{2}+3x-18, find the opposite of each term.

$$x^{2}+3x+2-x^{2}-3x-\left(-18\right)$$

The opposite of -18 is 18.

$$x^{2}+3x+2-x^{2}-3x+18$$

Combine x^{2} and -x^{2} to get 0.

$$3x+2-3x+18$$

Combine 3x and -3x to get 0.

$$2+18$$

Add 2 and 18 to get 20.

$$20$$

Factor

$$2^{2}\times 5$$