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

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

Evaluate

$$x^{2}+11x-6$$

Solution Steps

Multiply x-3 and x-3 to get \left(x-3\right)^{2}.

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

Apply the distributive property by multiplying each term of x+1 by each term of 2x+3.

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

Combine 3x and 2x to get 5x.

$$2x^{2}+5x+3-\left(x-3\right)^{2}$$

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

$$2x^{2}+5x+3-\left(x^{2}-6x+9\right)$$

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

$$2x^{2}+5x+3-x^{2}-\left(-6x\right)-9$$

The opposite of -6x is 6x.

$$2x^{2}+5x+3-x^{2}+6x-9$$

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

$$x^{2}+5x+3+6x-9$$

Combine 5x and 6x to get 11x.

$$x^{2}+11x+3-9$$

Subtract 9 from 3 to get -6.

$$x^{2}+11x-6$$

Expand

$$x^{2}+11x-6$$

Solution Steps

Multiply x-3 and x-3 to get \left(x-3\right)^{2}.

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

Apply the distributive property by multiplying each term of x+1 by each term of 2x+3.

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

Combine 3x and 2x to get 5x.

$$2x^{2}+5x+3-\left(x-3\right)^{2}$$

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

$$2x^{2}+5x+3-\left(x^{2}-6x+9\right)$$

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

$$2x^{2}+5x+3-x^{2}-\left(-6x\right)-9$$

The opposite of -6x is 6x.

$$2x^{2}+5x+3-x^{2}+6x-9$$

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

$$x^{2}+5x+3+6x-9$$

Combine 5x and 6x to get 11x.

$$x^{2}+11x+3-9$$

Subtract 9 from 3 to get -6.

$$x^{2}+11x-6$$