Properties of operations can be used to find an

expression that is equivalent to a given expression.

- Distributive Property
- The product of a number and a sum is equal to the sum of the number multiplied by each addend.

First, think of

*x* - 3 as

*x* + (-3).

7(*x* - 3) = 7[*x* + (-3)]

Next, multiply 7 by

*x* and -3, and add the products.

7[*x* + (-3)] = 7(*x*) + 7(-3)

Then, simplify.

7(*x*) + 7(-3) | = | 7*x* + (-21) |

| = | 7*x* - 21 |

So, 7*x* - 21 is equivalent to 7(*x* - 3).

Notice that 9 and 54 both have 9 as a factor. This means that the distributive property can be used to write an equivalent expression that is a product of 9 and a sum. This is called **factoring**.

First, write each term in the expression as a multiple of 9.

9*x* + 54 = 9(*x*) + 9(6)

Then, write the expression as a product of 9 and the sum of

*x* and 6.

9(*x*) + 9(6) = 9(*x* + 6)

So, 9(*x* + 6) is equivalent to 9*x* + 54.