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Simplifying Expressions and Combining Like Terms - Problem 1 17,935 views

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

Simplify an algebraic expression by combining like terms. Like terms have the same variable raised to the same exponent (or power). Identify the like terms by their variable form, then combine the coefficients. Remember when combining like terms that only the coefficients are combined, the variable form stays the same. A variable expression is in its simplest form when there are no more like terms to combine.

This problem tells me to combine like terms but I would do the same process and I would get the same answer if the directions said simplify the expression. Those are the same kinds of instructions and what you want to do when you're combining like terms is look for the same variables raised to the same exponents.

Like first, I'm given an x² so let's try to mark all the x squares and combine them. There's an x², there's another x² term and that's it. All together I have x² plus 4x² so I have 5x². The next thing I'm going to look for is the regular Xs. So there is a regular x and there's another regular x. Be really careful that I'm including the coefficients the 3 and the -2, 3 take away 2x is +1x. You don't have to write the 1, you can just write +x.

The last thing I haven't dealt with yet is what's called the constant term that 9, just +9 at the end there. So before you try these problems. One thing that I've done here, a strategy that I personally use is I use different markings like you see I underline the x²'s. I circled the Xs and then I just left the constants the same. For me personally that helps me to visually organize. I also can make sure that every term that I've given has been accounted for. I've counted if it's an x² it was added to the x²'s or whatever.

So when you're combining like terms look for the exponents and the variables. Make sure you don't lose the coefficients especially if they have a negative sign.