During the previous lesson we learned that we can use the distributive property to help us simplify algebraic expressions.

Let’s practice simplifying some expressions by first using the distributive property to prepare the expression.

After entering your simplified expression into the textbox, click the “Submit” button to see if your answer is correct.

Now, let’s move on with today’s lesson.

When an algebraic expression, such as x + 3x + 7, has two like terms adjacent to each other, it is easy to see that we can combine the terms to simplify the expression.

We do so by mentally applying the distributive property.

However, look at this expression: 6x + 3 + 2x. There are two like terms, but they are at opposite ends of the expression. We cannot use the distributive property in this case.

We solve this by using the commutative property to rearrange the second and third terms.

Now we can simplify the expression using the distributive property. The result is 8x + 3.

Here we have an expression, a + (3a + 8), which contains terms in parentheses. It has two like terms, a and 3a, but we can’t simplify it in its present form.

That is because one of the like terms is contained in the parentheses, while the other is not.

We can fix this by using the associative property to regroup the terms.

Now, we can simplify the expression by combining the terms contained in the parentheses. The result is 4a + 8.

Let’s do some practice. You are given an expression to simplify.

Select whether you will prepare the expression for simplification by using either the associative or commutative property.

After selecting your answer, click the “Submit” button.

Now, let’s work through a problem.

At the annual school rummage sale, three student clubs sold used music CDs.

The math club sold an unknown number of CDs, which we can represent by the variable n.

The science club sold 15 CDs.

The drama club sold eleven less than twice as many CDs as the math club.

Which of the following is an expression for the number of CDs sold by the drama club? Click the “Submit” button after selecting your answer.

The drama club sold 2n - 11 CDs. Now, we have expressions for the number of CDs sold by each of the clubs.

Which of the following is an expression for the total number of CDs sold by the three clubs? Click the “Submit” button after selecting your answer.

The total number of CDs sold by the three clubs is given by the expression: n + 15 + (2n – 11). However, it looks like it can be simplified.

First, let’s use the commutative property to rearrange the expression.

Which of the following is the expression we get after using the commutative property? Click the “Submit” button after selecting your answer.

We can rearrange the first two terms using the commutative property. This gives: 15 + n + (2n – 11).

Next, we can use the associative property to regroup the terms in the expression.

Which of the following is the expression we get after using the associative property? Click the “Submit” button after selecting your answer.

Using the associative property we regroup the middle two like terms. This gives: 15 + (n + 2n) - 11.

We then can simplify the expression by combining these terms using the distributive property. The resulting expression, 15 + 3n - 11, still can be simplified.

Which of the following is the final simplified form of the expression? Click the “Submit” button after entering your answer.

By using the commutative property once again, we rearrange the expression so that the number terms are together. This gives: 3n + 15 - 11

Combining the number terms, we then have the final simplified form of the expression for the total number of CDs sold: 3n + 4

Copyright 2006 The Regents of the University of California and Monterey Institute for Technology and Education