 This video is called multiplying binomials. We know this is a multiplication problem because between the two parentheses or between my two binomials there's no adding sign or subtracting sign or division sign so we know that there's an implied multiplication sign. Now when we have to do a binomial times a binomial or really any polynomials multiplied by each other it's important to remember that every term in the binomial on the left has to multiply with every term on the right so we do something called FOIL where we'll multiply the first terms together, the outside terms together, the inside terms together, and the last terms together. The FOIL, F-O-I-L, F-O-I-L can help you remember first outside, inside last, and some students have told me that they notice when you actually draw these lines connecting them you almost make a crescent moon so if you could imagine this being colored in yellow you've made a moon and that can kind of help you remember to pair up everything but the most important thing to remember is that everything in the left binomial has to multiply with everything in the right so when you multiply your first terms x times x you get x squared the outside terms 3 times x you get 3x, the inside terms 6 times x you get 6x and the last would be 6 times 3 to give you 18. Then you finish this up by combining like terms. I have like terms with my middle guys the 3x and the 6x so that will become 9x so we'll have x squared plus 9x plus 18 that would be my answer for multiplying those two binomials. Let's try another example again to simplify this multiplying first, outside, inside, last so you'll have 2x times x to give you 2x squared the outsides will be the 2x times 4 to give you 8x the insides will be 3 times x to give you 3x and the last will be 3 times 4 to give you 12 so again always ask yourself if you have any like terms to combine I've got an 8x and a 3x to become 11x so I have 2x squared plus 11x plus 12 and that will be my answer for multiplying binomials together. Let's try another one here we go to simplify to do the first 5m times 8m will be 40m squared 5m times negative 1 is a negative 5m 2 times 8m is a positive 16m and 2 times negative 1 is a negative 2 I have like terms here that I need to combine I have a positive 16m and a negative 5m so I'll have my 40m squared negative 5 plus 16 is a positive 11m and then the minus 2 at the end this answer right now is in standard form and I've combined all like terms so that would be done example before we conclude this video we have multiplying the first the outside the inside and the last 6h times 2h is excuse me is 12h squared 6h times 3 is a plus 18h a negative 7 times 2h is a negative 14h and a negative 7 times 3 is a negative 21 so we have a few like terms that we have to combine I have a negative 14h plus 18h so I've got a 12h squared 18 minus 14 is a positive 4h minus 21