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

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

Evaluate

$$6\left(x+2\right)$$

Solution Steps

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

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

Combine 3x and 3x to get 6x.

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

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

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

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

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

The opposite of -3x is 3x.

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

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

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

Combine 6x and 3x to get 9x.

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

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

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

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

$$6x+3+9$$

Add 3 and 9 to get 12.

$$6x+12$$

Expand

$$6x+12$$

Solution Steps

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

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

Combine 3x and 3x to get 6x.

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

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

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

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

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

The opposite of -3x is 3x.

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

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

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

Combine 6x and 3x to get 9x.

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

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

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

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

$$6x+3+9$$

Add 3 and 9 to get 12.

$$6x+12$$