Factor by Grouping

hey welcome back to M math today we are going to look at the second type of factoring which is factoring by grouping okay when do you use factoring by grouping you use it when you have four terms you've got too many so you need to make them divide them into small groups so I'm going to group mine the first two together and then the back two together and the back two I'm going to include the sign with this third term right here okay so now I'm just going to look for a GCF so let's try to find the GCF of each group let's see the GCF of 3x cubed y^2 and 15 XY hm say that would be a three and x to the first Power and a y to the first Power because when you're factoring out gcfs you want to take the lowest exponent okay we're dividing each one by the GCF so I'm going to write a 3xy under each term let's see that's going to leave me with an x^2 y minus let's see it's going to give me five the x's and the Y's are gone okay now I do that with the first group now I'm going to ignore my first group and I'm just going to focus on the second binom on these two terms what's my common factor here well let's see eight goes into both 40 and itself so let's take at a positive 8 and you always want to take out whatever sign that is and then I have an X2 Y and this one doesn't have any variables so I actually can't take out any variables at all just a coefficient so once I divide those let's see my eights are canceled and I'm left with x^2 y minus well 8 40 / 8 is 5 Okay so let's see what we have we've taken out a GCF out of each of the two original groups and now notice what's left in parentheses x^2 y - 5 x^2 y - 5 so these are now common factors so let's take add an x^2 y - 5 and see what we have left once we factor that out well what's left is 3xy + 8 3xy + 8 and there we go we are done factoring by grouping thanks for watching and you may enjoy this next video on a different way to factor