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

$$( 1 ) ( x - 2 ) ( x + 3 ) - ( x + 3 ) ^ { 2 }$$

Evaluate

$$-5x-15$$

Solution Steps

Use the distributive property to multiply 1 by x-2.

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

Use the distributive property to multiply x-2 by x+3 and combine like terms.

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

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+3\right)^{2}.

$$x^{2}+x-6-\left(x^{2}+6x+9\right)$$

To find the opposite of x^{2}+6x+9, find the opposite of each term.

$$x^{2}+x-6-x^{2}-6x-9$$

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

$$x-6-6x-9$$

Combine x and -6x to get -5x.

$$-5x-6-9$$

Subtract 9 from -6 to get -15.

$$-5x-15$$

Expand

$$-5x-15$$

Solution Steps

Use the distributive property to multiply 1 by x-2.

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

Use the distributive property to multiply x-2 by x+3 and combine like terms.

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

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+3\right)^{2}.

$$x^{2}+x-6-\left(x^{2}+6x+9\right)$$

To find the opposite of x^{2}+6x+9, find the opposite of each term.

$$x^{2}+x-6-x^{2}-6x-9$$

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

$$x-6-6x-9$$

Combine x and -6x to get -5x.

$$-5x-6-9$$

Subtract 9 from -6 to get -15.

$$-5x-15$$