10.3 a factoring tricks perfect squares now you may recall when we were multiplying polom that when we had a polinomial in this form it multiplied out to a 2 + 2 a B plus b^ 2 if we can take the square root rid of the first and last term it may be a what we call a perfect square trinomial okay let's see how this works so when I look at example one one of the first things that pops out at to me is that I can take the square < TK of 25 I can also take the square Ro T of one it's a given that we can do the x s part in general so what that means is that this may be a perfect square trinomial so what I'm looking for here if you remember back to our formula we have a 2 + 2 a b + B squared now this right here I should write it as a plus or minus because this can either be positive or minus in this case we have minus here so we're looking to see is we're checking the middle term is 2 * the square Ro T of our a which is in this case is one time the square OT of 25 going to give me 10 that's what we're looking for specific quickly well just so happens it does the square root of we have 2 * 1 * the < TK of 25 which would be five that gives me 10 that means that it is a perfect square trinomial this is kind of my scratch work here so we're going to put a square on the outside we bring down this sign here which is negative the square root of the first term is x the square root of the last term is five and we are done how would I check it remember that any times you fa Factor anything you can check your answer by foiling it back out okay good habit to develop let's look at our second one here again I can take the square root of N and I know I can take the square root of 25 for the most part we just kind of ignore the variables as long as we have squares there we know we're good so we're looking to see if 2 * the square < TK of 9 * the sare < TK of 25 is going to give us 30 well I have 2 * 3 * 5 well guess what I get 30 so that tells me it is a perfect square trinomial the fun part of course is recognizing these when they are not um identified as perfect square trinomials when they're scattered in the homework again the key is to look at your first term and your last term to see if you can take square roots you're going to use Middle math for this part right here and if it you know it works out to be the middle term then you guess what you put your boxes I'm going to put in my X and my y those are no question there this this is a plus so I'm going to put down a plus Square < TK of 9 is 3 Square < TK of 25 is 5 and make sure the whole thing is raised to the second power and you're done