Solve x(x+3)+3(x+3)-x(x-3)-3(x-3)

$$x(x+3)+3(x+3)-x(x-3)-3(x-3)$$

Evaluate

$$6\left(x+3\right)$$

Solution Steps

Use the distributive property to multiply x by x+3.

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

Use the distributive property to multiply 3 by x+3.

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

Combine 3x and 3x to get 6x.

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

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

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

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

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

The opposite of -3x is 3x.

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

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

$$6x+9+3x-3\left(x-3\right)$$

Combine 6x and 3x to get 9x.

$$9x+9-3\left(x-3\right)$$

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

$$9x+9-3x+9$$

Combine 9x and -3x to get 6x.

$$6x+9+9$$

Add 9 and 9 to get 18.

$$6x+18$$

Expand

$$6x+18$$

Solution Steps

Use the distributive property to multiply x by x+3.

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

Use the distributive property to multiply 3 by x+3.

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

Combine 3x and 3x to get 6x.

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

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

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

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

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

The opposite of -3x is 3x.

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

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

$$6x+9+3x-3\left(x-3\right)$$

Combine 6x and 3x to get 9x.

$$9x+9-3\left(x-3\right)$$

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

$$9x+9-3x+9$$

Combine 9x and -3x to get 6x.

$$6x+9+9$$

Add 9 and 9 to get 18.

$$6x+18$$