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Simplifying Expressions and Combining Like Terms - Problem 3

Teacher/Instructor Alissa Fong
Alissa Fong

MA, Stanford University
Teaching in the San Francisco Bay Area

Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts

Given a triangle with three sides, the perimeter is the sum of the three sides. Set up an expression by adding the three sides together. Simplify the expression by combining like terms. Remember that like terms are terms with the same variable raised to the same exponent (power). Combine like terms by combining the coefficient and leaving the variable form the same.

Even though you guys are taking a course called Algebra a lot of the times you'll be asked to use what you know about other courses like Geometry. Look at this problem. It asks us to find the simplified form of the perimeter of this triangle. So in order to do this we have to remember what perimeter means. Do you remember? That's right, perimeter means you've got to add up all the sides.

So what I'm going to do is write out a long expression and then simplify it. So this side is 5-x, I need to add all the other sides so add 4x and then add 2x minus 3. That's the perimeter but it's not simplified yet. So let's go through and simplify. The way I do it is by marking all of the like terms like let's start with the Xs first. I have a -x, a +4x and a +2x. -1x plus 4 would be +3 plus 2 more is 5x and then in terms of my constants I have 5 take away 3 which is going to be 2. So the expression for my perimeter would be 5x plus 2.

Even though you guys aren't in geometry class, when you come to problems like this you know are geometry don't just skip them, you guys can do it. Usually they are based on words and concepts that you've learned before.

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