Simplifying Expressions with Like terms

[one speaker]

Narrator: We are asked to simplify the following expression. [5a-2b-6+3a+6b] So we’re going to start by writing this so that our terms, our like terms, are next to each other. So I’m going to write this as 5a plus 3a minus 2b plus 6b minus 6.[5a+3a-2b+6b-6] So you can see that I’ve still got all the parts in the equation, but I’ve written them so I can see where my like terms are. Now, remember that 5A, let’s just take a minute to remember 5a plus 3a. Well, that can be rewritten as a plus a plus a plus a plus a, five times. So that’s 5a, and 3a can be written as a plus a plus a. So if I combine all those together, then I have 8a, so I’m basically adding my coefficients to find out how many  I have. [5a+3a=(5+3)a=8a] So, in this case, 8a. So, that’s a little side note. So now if I know I’m adding my coefficients I can write this as 5 plus 3 inside a parenthesis times a plus negative 2 plus 6 time b minus 6. [(5+3)a+(-2+6)b-6] So I’m going to add my coefficients here to get 8a plus, I’m going to add my coefficients here to get 4b, then I still have minus 6. [8a+4b-6] Now, because I don’t have anymore like terms, I’m done. So the answer is 8a plus 4b minus 6.      

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