In the previous lesson we learned about the associative, commutative, and distributive properties. Let’s take a short review.

Click the “Submit” button after entering your answer.

Now, let’s continue with today’s lesson.

Sometimes, an algebraic expression can be rewritten, or simplified, to a form that is usually smaller than the original. Here 2x + 3x - 5 can be simplified to 5x - 5.

We can think of three types of expressions. The first type is one that cannot be simplified at all.

The second type is an expression that can be simplified directly. Here we simply combined the first two terms, 3y and -y, to make the single term 2y.

The third type requires some sort of preparation through the use of one or more number properties before it can be simplified. Here, z – 5 + 3z is simplified to 4z - 5 after using the commutative property.

In this lesson we will look only at expressions of the first two types. Expressions of the third type will be covered in future lessons.

Now let’s look at some examples of expressions that can or cannot be simplified.

In each case, choose whether or not the expression is in simplest form by clicking on the “Yes” or “No” button.

Let’s look at the process of simplifying an expression. Here we have a basic algebraic expression: y + 8 + 2x + 4x

We can combine the last two terms because they are like terms. Like terms are terms that contain the same variable.

We combine like terms by adding their coefficients, the numerical factor in front of the variable.

The resulting expression, y + 8 + 6x, has no more like terms, so it cannot be simplified any more.

The variables in like terms must have the same power. Here, <EQUATION> can be simplified to <EQUATION>.

In this example, the first two terms have the same variable, but they are not like terms because they have different powers.

The expression, <EQUATION> is already in its simplest form.

Now, let’s do some practice identifying like terms.

In each case, choose whether or not the two terms shown are like terms, or not, by clicking on the “Yes” or “No” button.

There may be multiple like terms we can simplify in an expression, such as in this one: y – 3y + 5y + 12

Here, the first three terms can be combined to simplify the expression. The result is 3y + 12.

Now, let’s practice simplifying some expressions.

After entering your simplified expression into the textbox, click the “Submit” button.

Now, let’s use what we have learned so far in this course in the following problem.

Malcolm is four pounds less than twice the weight of his sister Marlene.

Let’s have the variable w represent Marlene’s weight.

Which of the following is an expression for Malcolm’s weight? Click the “Submit” button after selecting your answer.

We have an expression for Malcolm’s weight: 2w - 4. Now, suppose we are interested in an expression for the total weight of both children.

We can do this by adding the expression for Malcolm’s weight to Marlene’s weight, w.

Now, which of the following is a simplified expression for the total weight of Malcolm and Marlene? Click the “Submit” button after selecting your answer.

Combining like terms, we have an expression for the total weight of the two children: 3w - 4

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