Factoring Expressions - Free Educational videos for Students in K-12

Factoring Expressions - By Anywhere Math

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00:0-1	Welcome anywhere , Math . I'm Jeff Jacobson . And
00:01	today we're gonna talk about factoring expressions . Let's get
00:05	started . Alright . Example one factor 20 minus 12
00:27	. Using the G . C . F . Now
00:29	, if we're factoring obviously we're gonna be talking about
00:33	factors . Uh And if you think of factors you
00:36	probably are going to be thinking of greatest common factor
00:40	. So first , if we're gonna factor using the
00:43	G . C . F . We need to find
00:44	the factors of 2012 . Well the factors of 20
00:49	, you've got one And 20 , you've got two
00:54	and 10 . Three doesn't work . Four does four
00:59	times five works Six ? No seven . No .
01:03	Eight . No . 9 . 10 . And were
01:06	there . So there's the factors of 20 . All
01:08	right , how about the factors of 12 ? Well
01:10	, for 12 , same thing one times 12 to
01:13	23 . So those are the factors of 12 .
01:18	What can 12 B divided by evenly . So now
01:22	the greatest common factor , they both have a one
01:24	, so that's a common factor . They both have
01:26	a two . That's a common factor . Three .
01:28	No , they both have a four , that's a
01:31	common factor . Are there any others that are in
01:33	common ? No , So four is the greatest common
01:37	factor . Hopefully this is his review . What that
01:40	means is we are going to factor out the four
01:44	from these two numbers , so you can think of
01:48	this as kind of the reverse of the distributive property
01:53	. When we use the distributive property , we multiply
01:57	whatever we're distributing to every term in the parenthesis .
02:02	What we're doing now is we're factoring out or we
02:04	are dividing each term by the greatest common factor .
02:09	So let me show you what I mean , 20-12
02:13	. Well , we can think of 20 as four
02:16	times five minus 12 as four times three . And
02:22	like we said earlier , we know that four is
02:24	a common factor , that's why I chose that .
02:26	So what I'm gonna do is I'm gonna divide that
02:28	out , I'm gonna factor it out And now I'm
02:34	just going to have what's left , which is 5
02:38	-3 . So you can think of this as very
02:41	similar to the distributive property . Just kind of in
02:44	reverse . If we use the distributive property here ,
02:47	I would do four times five , which is 20
02:51	-4 Times three , which is 12 . But we
02:54	just did the opposite , which is called factory .
02:56	Here's what to try on your own . All right
03:04	, Here's example to back to the expression using the
03:07	G c F . So , we're still factoring however
03:10	, you probably notice that these examples are no longer
03:13	numerical expressions . Now , we're using algebraic expressions ,
03:17	but we do the exact same thing . We're looking
03:20	for those common factor and specifically the greatest common factor
03:24	that we can factor out of the expression or divide
03:28	out . Um And then we make those parentheses .
03:32	So here , if you notice , well , I've
03:34	got 36 W . and nine . Um There is
03:37	no w here , so W is not going to
03:40	be part of my G . C . F .
03:42	I'm mainly going to focus on the nine uh and
03:45	the 36 . And I think , well what is
03:47	the greatest common factor of nine and 36 ? Well
03:52	it's not right . So if I think about 36
03:56	W . as nine times four W . Right ?
04:03	nine times 4 w is 36 W Plus and nine
04:07	, I can think of nine times one . I
04:11	am going to factor out that night and as you
04:15	go along , you probably won't have to do this
04:18	step . Hopefully you'll be able to do it in
04:20	your head . But for now let's just write it
04:22	down so it helps . I factor out that nine
04:26	, I'm dividing both terms by that nine That comes
04:30	out . So what's left over while I've got the
04:32	four W . Plus what ? And that is a
04:39	factor . And if I want to check it ,
04:42	just do the distributive property . Do the opposite nine
04:45	times four . W . Is 36 W . Plus
04:48	nine times one is nine . There we go .
04:52	I am happy with that . Let's look at B
04:54	. 28 X plus 21 . Why ? Again This
04:59	term has the next this term has a why ?
05:01	So those are going to be part of what I'm
05:04	factoring out . I'm just gonna focus on the 28
05:07	and 21 . What's the greatest common factor of 28
05:10	and 21 seven ? So 28 X . I'm gonna
05:15	think of as seven times four X . seven times
05:20	4 . x . 28 x plus the 21 .
05:23	Y . Seven times three Y . Seven times three
05:28	Y . is 21 . Why ? So notice I'm
05:31	not changing the value here at all . Right .
05:34	Um these are all gonna these are all gonna be
05:37	equivalent expressions . Um No nobody's changing the value .
05:41	We're just changing what it looks like . That's all
05:42	we're doing . Um So now let's divide out that
05:48	seven from from both terms . Let's factor it out
05:52	. So I've got seven times 4 x . Plus
05:58	three . Why ? Yeah . And again if I
06:01	want to double check just use the distributive property seven
06:04	times four X . Is 28 X plus seven times
06:08	three Y . Is 21 . Why box that ?
06:13	And let's move on to the last one . Which
06:15	is a little challenging . So now you've got three
06:18	X . Squared and 12 X . Well right away
06:23	um you probably say well the three and 12 greatest
06:26	common factor is three . That's not bad . But
06:30	is there a common factor between the X . Squared
06:34	and the X . And if you think well what's
06:36	X . Square X . Square just means X .
06:39	Times X . And then you've got an X .
06:42	Is there a factor in common ? Of course there
06:45	is annex . So we are going to factor that
06:49	out as well . Let's let me show you what
06:54	I mean . So we're already factoring out the three
06:57	. We're also going to factor out the X .
07:00	So together we factor out the three X . Well
07:05	what's left over ? If I divide three X squared
07:09	by three X . What's left over ? Just an
07:12	X . And if I check three x times x
07:17	is three x squared X . Times X . Will
07:20	give you the X square plus . Do the same
07:25	Factor out the three eggs . Yeah three X times
07:31	. What is going to give me 12 X .
07:32	Well what's left over just before three X . Times
07:36	four is 12 x . Now we are putting it
07:39	all together . I factor out the three X .
07:42	From both terms . Bring it outside the parentheses so
07:45	I've got three X . What's left over ? The
07:48	X plus four . And before I box my answer
07:53	, let me check . Using the distributive property .
07:56	Three X times X . Is three X squared plus
07:59	three X times four is 12 X . Now I
08:03	can box it and I'm done . Here's some to
08:07	try on your own as always . Thank you so
08:15	much for watching and if you like this video please
08:17	subscribe .

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