Hippocampus Algebra: Using the distributive property

In the previous lesson we learned that some expressions can be simplified, usually to form smaller expressions.

Let’s review simplifying some basic expressions.

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

After comparing answers, click the “Next” button to continue.

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

Previously, we learned to simplify an algebraic expression by combining like terms that appeared together, as in this example where 4x + 2x + 9 simplifies to 6x + 9.

When we did this, we actually were rewriting the expression mentally by using the distributive property.

We can use the distributive property in a more direct manner to simplify an expression containing terms in parentheses, such as the one here: 3(2y – 4)

Using the distributive property we eliminate the terms in parentheses This leaves the new expression, 6y - 12, which is in simplest form..

Now let’s look at some examples of expressions that can be simplified by using the distributive property.

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

Sometimes, using the distributive property is a way to prepare an expression for further simplifying. Look at this example: a + 2(a – 3) + 10

First, we use the distributive property to eliminate the parentheses.

Now, we see that we can combine the last two number terms.

Finally, we can combine the first two like terms. This gives us the expression in its simplest form: 3a + 4

Now, let’s do some practice simplifying expressions.

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

Now, let’s look at an example problem. Teams from Washington, Lincoln, and King High Schools competed in a gymnastics meet.

King High School’s team scored 24 points less than twice the score of Washington’s team.

Let’s have the variable x represent Washington High School’s team score.

Which of the following is an expression for King High School’s team score? Click the “Submit” button after selecting your answer.

We have an expression for the number of points scored by King High School’s team at the gymnastics meet: 2x - 24

Now, we discover that Lincoln High School’s team scored half as many points as King High School’s team.

Which of the following is an expression for the number of points scored by Lincoln High School’s team? Click the “Submit” button after selecting your answer.

The expression, 0.5(2x – 24), gives the points scored by Lincoln High School’s team. It contains terms in parentheses. Maybe we can simplify it.

Which of the following is a simplified expression for the number of points scored by Lincoln High School’s team? Click the “Submit” button after selecting your answer.

The simplified expression is x - 12. We see that Lincoln High School’s team scored 12 points less than Washington’s team.