How to Simplify Expressions Using the Order of Operations

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Simplifying algebraic expressions should be no different than simplifying any other kind of expression. Simplify expressions using the order of operations with help from an experienced mathematics professional in this free video clip.

Part of the Video Series: Math Calculations
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Hi, I'm Drew Moyer and this is how to simplify expressions using order of operations. Simplifying algebraic expressions should be no different than simplifying any other kind of expression. I have to use the order of operations which is PEMDAS. So here is our expression, we have 2 bracket, A quantity 8A plus 5 plus 2A quantity A minus 7 squared. The first thing I want to do is the P which stands for parentheses, I want to simplify everything that I can within the parentheses first. So, I have 2 bracket, then I want to distribute this A to both the A and the 5 which will give me A squared plus 5A and then I'm going to do the same thing over here. I'm going to distribute this 2A to this A and this minus 7 plus 2A squared minus 14A all squared. Now within these parentheses I can combine like terms. I have some A squared and I have some regular As. So I have 2 bracket, 3A squared minus 9A all squared. Now that is as simple as I can get it within the parentheses so I'm going to move on to my next step, exponents and you can see I have an exponent right here on the outside. So what this literally means is it means two of these brackets multiplied together. So I have 2 bracket, 3A squared minus 9A bracket and another bracket of the same thing. And now I can use foil to get both of these within one bracket. So this 2 is still on the outside, I haven't messed with it. First I would multiply these two together which gets me 9A to the 4th, then I would do the outside terms which is 3A times negative, 3A squared times negative 9A which is -27A cubed. Then the inside terms, negative 9A times positive 3A squared which is again negative 27A cubed and then the last terms which is negative 9A times negative 9A, positive 81A squared. And now I've taken care of the exponents. So all that's left to do is to distribute this 2 all the way through to every term inside the brackets. So I have 18A to the 4th minus 54A to the third minus 54A to the third plus 162A squared. And my last step would be to do any addition or subtraction and I can combine these two like terms. So I have 18A to the 4th minus 108A cubed plus 162A squared and that is as simple as I can get it without knowing what my value for A is. I'm Drew Moyer, and this has been how to simplify expressions using order of operations.

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