Simplifying Variable Expressions 02:53 minutes

Video Transcript

Transcript Simplifying Variable Expressions

Algebraic expressions with more than one variable can look scary. To make variable expressions easier to solve, simply simplify! Don't be frightened; I will walk you through the steps.

You can only add and subtract like Terms

This expression has two different variables: 3x + 2y. Hmm… How do you simplify this expression? Maybe you're thinking 3x + 2y = 5xy. STOP! This is wrong! You can't simplify this expression anymore. Combining terms with x and terms with y is not possible.
It's almost as wrong as Dr. Evil attempting to create a “Sharkuine” – by combining a shark with a penguine! Just like sharks and penguins, variables such as x and y are not the same. Repeat to yourself: You can only add and subtract like terms! When adding and subtracting variables, never, ever combine unlike terms. Never, ever!

Example how to simplify Variable Expressions

Let’s try out this example. We will go step by step. x + 3 · (10 + y) − 7x − y.

  • Step 1 is to write out the expression as a sum. See the parentheses? You will need to use the Distributive Property to multiply the three times the binomial contained inside the parentheses. Now you have: x + 30 + 3y − 7x − y.
  • Step 2 is to group the like terms. You can use the Commutative Property to move the terms. Place the x’s with x’s, the y’s with y’s, and so on. This will make the next step easier: x − 7x + 3y − y + 30.
  • Now, Step 3 is to simplify the expression by combining the like terms. For terms that have numbers and variables, remember the coefficient tells us how many there are of each variable: −6x + 2y + 30.

Ok, let’s go over this one more time:

  • Step 1: Write the expression as a sum. If there are parentheses, use the Distributive Property.
  • Step 2: Move the terms around to group the like terms by using the Commutative Property.
  • And lastly, Step 3, simplify the expression by combining the like terms.

Most important: Never, ever try to combine unlike terms. Here is your reminder: Don’t create sharkuins! Don’t make the same mistake as Dr. Evil. He had to learn the hard way.