Expand and Simplify Binomial Expressions


Start with a you go, a times b and a times c but we also have to do the same thing for d so we do d times b and we also do d times c so we do a times b so it looks like this I’ll rub this off.

So basically you do a times b and c so there’s basically this whole bracket so I did a times b plus c and then you do d times b plus c so see how I did d times b plus c so now you go ahead and expand it out so then you do a times b and a times c and then d times b and b times c like you always do so ab, ac plus db or bd because I like to keep it in that alphabetical order and then dc but cd rather, so a times this whole bracket and three times this whole bracket okay

So if I separate it, it looks like this times that bracket plus three times that bracket okay, and then you do your normal thing times a, times negative two so that’s a squared a time a is a squared a times negative 2 is negative 2a and then 3 times a, 3 times negative 2.

So 3a minus 6. Make sure it’s a negative 6 because positive negative makes a negative okay so again be careful with the signs now are there like terms guys can we gather anything up together?

Yes we can look at these we’ve got a negative 2a and we’ve got a 3a, a is common so that’s going to be my like terms so we have a squared minus 2a plus 3a is just positive a, and then we have minus 6 at the end because that’s we can’t we don’t have any more like terms other than the right so what I would do is multiply the 2a with the big bracket and the 5 with the bracket so if I separate it out I get 2a times a minus 1 plus 5 times a minus 1 and expand it out so 2a times a is 2a squared, 2a times negative 1, negative 2a and here 5a minus 5 Okay?

And then gather up your like terms the only like terms I have are these the ones with the so 2a squared remains minus 2a plus 5a is positive 3a and then we stick the negative 5 at the end and that’s it


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