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.

- Like Terms
- Terms that have the same variables.

First, distribute the 5.

5(10*x* - 16 + *x*) + 19 = 50*x* - 80 + 5*x* + 19

Then, combine like terms.

50*x* - 80 + 5*x* + 19 | = | (50*x* + 5*x*) + (-80 + 19) |

| = | 55*x* + (-61) |

| = | 55*x* - 61 |

So, 55*x* - 61 is equivalent to 5(10*x* - 16 + *x*) + 19.

Distribute the 3

*r*.

3*r*(*s* - 7 + 8*t*) = 3*rs* - 21*r* + 24*rt*

There are no like terms in this expression.

So, 3*rs* - 21*r* + 24*rt* is equivalent to 3*r*(*s* - 7 + 8*t*).