Multiplying and Distributing Radical Expressions - Problem 3

Here I have 2 binomials that both have square roots in them. In order to multiply them, I’m going to be using the FOIL process multiplying the first, outers, inners and lasts and then combining like terms.

So if I multiply my firsts 4 times 3 is 12, that’s the easy part. Outers 4 times negative root 6, Inners 3 times positive roots 6, lasts is going to be root 6 times negative root 6, or negative root 36. Some of you guys will right away be able to recognize that that’s going to be -6.

Okay so let’s combine like terms in the middle, -4 root 6 plus 3 roots 6 is -1 root 6. The last thing I’m going to combine is my firsts and last. I have 2 integers 12 and -6. When I combine them my final answer will look like 6 take away root 6. That can be simplified any further. You might be tempted to like factor out the 6 or something, but in fact 6 is not a common factor of both of these guys. It’s confusing because 6 is under the radical sign. We can’t do anything with it.

This is the final answer to that product. Again the most common mistake students will make is right here. They’ll forget that negative sign. They’ll recognize that square root of 6 times square root of 6 is 6, but they’ll lose that negative sign that came from our second binomial. So be careful with those negatives and then combine all your like terms to get that final answer.