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# Factoring two-variable quadratics: grouping

CCSS.Math:

## Video transcript

we're asked to factor this expression by grouping now they mention grouping we're going to see what grouping is but we're going to see very quickly that we have to do this thing called grouping because you can't just factor this expression if you look at these each of the terms all but one of them is divisible by five so you can't just you can't just factor out a 5 not all of them are divisible by either R or s this is only divisible by r that's only divisible by s that's divisible by neither so there is no common factor across all four of these terms that's what we have to group them into groups where there are common factors and then see if that simplifies the whole thing and there is a little bit of an art to recognizing when you can factor by grouping but they've set this problem up nicely for us so if you look at if you look at well let's look at these first two terms right here you have a 5r s and a 25 are these two guys clearly have some common factors they're both divisible by five they're both divisible by R so if I just wanted to if I just wanted to factor this one out or if I wanted to rewrite it as a product of two expressions how could I write it well I could write it as a product of five R times what's five RS divided by five R well you just don't have an S left over you just have an S there plus what's 25 R divided by five R well 25 divided by 5 is 5 and r divided by r is just 1 so 25 R over five R is 5 so these first two terms can be factored into these two expressions and then let's look at the second two terms look at the second two terms well they definitely have a common factor you have a negative 3 or a positive 3 common to both of these let's just go with the negative 3 and our goal is really to factor it into a negative 3 times hopefully something very similar to S Plus 5 and you might already be seeing that it's going to factor into S Plus 5 so let's factor out that negative 3 so these two terms can rewrite as negative 3 times what's negative 3 s divided by negative 3 well you're going to have an S left over just going to have an S and that's what's negative 15 divided by negative 3 well that's just positive 5 that is just positive 5 and just like that we've Group and we were able to factor each of those groups and then something interesting might pop out at you and one you can always verify that you factor this properly by distributing by distributing each of these expressions distributing the five R times s plus 5 and the negative 3 times S Plus 5 you'll get exactly this but something maybe jumped out at you just now if five R times S Plus 5 then you have negative 3 times s plus 5 so now this expression we have two terms instead of four right this is one term this is another term and they both have s plus 5 as a common factor so we can now factor out s plus 5 we can now factor out s plus 5 so this whole thing can be re-written as S Plus 5 times times what times 5r right if you take five R times s plus five and you factor out the S Plus 5 you're just left with the 5r and then similarly if you take negative three times s plus five and you factor out the S Plus 5 or divided by s plus five you just have a negative three just like that and then we're done we've factored this expression by grouping its s plus five times five R minus three and you can verify it by multiplying it out if you distribute the S Plus 5 onto each of these onto each of these terms you'll get this expression up here and then if you distribute the five R over there you're going to get that expression if you distribute the negative three you're going to get that expression so this does simplify that so we have factored it