thanks for stopping by this is two minute classroom and today we're talking about how to multiply binomials like these using the foil method you'll use the foil method to turn two binomials like these into their quadratic polynomial or standard form like so foil stands for first outer inner last but you probably already knew that you use it to multiply each term in one expression by each term in the other expression let's work through a few examples we'll start simple multiply X plus 2 by 2 X plus 3 we start by multiplying the first two terms together so x times 2x equals 2x squared next we multiply the outer terms x times 3 equals 3x then we multiply the inner terms together 2 times 2x gives us 4x and finally we multiply the last 2 terms together 2 times 3 gives us 6 now we have the equation 2x squared plus 4x plus 3 X plus 6 all that is left to do is combine like terms in this case the sum of 4x and 3x which gives us 7x so we end up with 2x squared plus 7x plus 6 simple right but there are some tricky questions you may encounter for example if you're asked to solve the expression 3x plus 4 squared what do you do first you split the equation into two binomials so a 3x plus 4 times 3x plus 4 then you just use the foil method first outer inner and notice the outer and inner products are the same when you're solving for a square and last this gives you nine x squared plus twelve X plus 12 X plus sixteen then combine like terms and you should end up with nine x squared plus 24x plus 16 another tricky situation is when negative numbers are involved for example X plus 1 times 2 X minus 3 don't panic just use the foil method and whenever you use this 3 it should always be negative so real quick first outer inner last put them together and get 2x squared minus 3x plus 2x minus 3 and combine like terms to get 2x squared minus X minus 3 if you have any tests or quizzes coming up in any of your classes you'll want to watch my test prep playlist or watch this video that YouTube thinks you'll enjoy thanks for watching and I'll catch you next time [Music]