Simplifying Algebraic Expressions
There are two things that you must be able to do when simplifying algebraic expressions. The first is to be able to use the distributive property.
The second math concept that you must understand is how to combine like terms.
So, what are like terms? Let's start first with just the word, term and a few other vocabulary words!
Take a look at the 8 terms above. (2x is a term, 5y is a term, 7 is a term...)
The 4 and the 7 do not have a variable. They are called constants. Since they don't have a variable, their values will always remain the same, 4 and 7. That's why they are called constants.
The 2 in the term 2x is called a coefficient. A coefficient is a number by which a variable is multiplied. The 5 in the term 5y is a coefficient; The 3 in the term 3xy is a coefficient.
Can you guess which other terms have coefficients?
Yes, you are right, the 8 in 8x, 6 in 6y, and the 4 in 4x2.
Ok.. now moving onto like terms. Like terms are two or more terms that have EXACTLY the same variables. (The coefficients do not have to be the same, just the variables!)
For example, for the 8 terms above, 2x and 8x are like terms because they both just contain an x.
Can you find the other two sets of like terms?
Yes, 5y and 6y are like terms. 7 and 4 are like terms because they are both constants.
3xy does not have a like term because no other term has the variable x and y. 4x2 does not have a like term because no other term has x2.
Ok, enough vocabulary... let's look at a few examples. We are going to simplify each expression by combining like terms.
TIP: When you combine like terms, you MUST take the sign in front of the term with it or your answer may be incorrect!
Ok, are you confident enough to use the distributive property when simplifying algebraic expressions? Sure you are, let's go!
If you see an addition or subtraction problem inside a set of parenthesis, you must use the distributive property BEFORE simplifying the expression.
As you review the next 2 examples, notice how the distributive property was used first, then the algebraic expression was simplified.
Ok... with four great examples, you should be ready to try some on your own!
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