Mistake 1- Distributing Incorrectly

Here is the number one common mistake of college algebra students. A lot of times what happens is that students will see this 2 and assume that it will distribute through here and here. What a lot of students will come up with is they'll say x squared is x squared plus and 5 times 5 is 25. Be really careful about this. This is very, very incorrect. Let's actually see how to do it the correct way. So, let's say that we've got this x plus 5 squared. This 2 up here actually means that it's x plus 5 times x plus 5. Of course we have to use that mnemonic device of FOILing. Using the distributive property we’ll say, okay, I've got x times x which is equal to x squared. Then I have x times 5 which is equal to 5x. And then 5 times x, it’s still plus 5x and then 5 times 5 is 25. Adding together like terms we get x squared plus 10x plus 25. So you have to be really, really careful with the distributing property. I think a lot of times the student gets mixed up with the idea that the only time you can actually distribute a 2 that's in a power is if you have something like this. Say if you have 5x and then this is squared. Well, what happens is that, yes, with this, this actually means 5x times 5x which equals 25x squared. So, what you can do is that the shortcut for this, just by knowing your rules for exponents, is this would distribute through here. But notice it's a multiplication not an addition or subtraction. So you can only do that when it's multiplication. So you can say that this is actually 25 and then times x squared. But that's the difference between the two. Make sure that if you are going to distribute a power that you actually have a multiplication symbol in there. Otherwise, you’re going to have to use the distributive property, using that mnemonic device of FOILing out the first, the outer, the inner, and then the last.