02 - Simplifying Expressions That Involve Sums And Differences, Part 2
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hello welcome back to algebra 2 we're
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continuing to work on simplifying
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expressions that involve addition and
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subtraction we're just getting more
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problems practice with problems slightly
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more complex but really it's all the
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same thing also I've erased the order of
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operations and all that from the board
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because we're growing up a little bit
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now and we need to start committing that
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to memory so I'm not gonna be
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referencing it but you will get the hang
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of it by solving lots of problems so
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let's just dive right into the first
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question
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4 times P minus 2 Q now I'm gonna tell
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you right now even though I said this is
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involving a simplifying expressions
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involving addition and subtraction I
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don't mean that there will never be any
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multiplication I just mean that most of
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these problems are going to be focusing
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on the adding and subtracting aspect
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later on we'll do some review problems
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that focus more on the multiplication
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and division so you can see here that
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you have something inside the
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parentheses you would normally work on
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that first as to the order of operations
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however these are unlike terms you have
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a P term and a Q term so I can't really
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subtract them I can't do anything with
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that what I do have is a 4 in the
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outside which I can distribute the 4 in
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for times P is 4 P the minus sign comes
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along for the ride 4 times 2 is 8 and
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yeah thank you so another way to think
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of it as 4 times P is 4 P 4 times
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negative 2 remember positive times
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negative that gives you negative 8 and
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then the Q comes along for the ride so
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you get 4 P minus 8 Q you can't add
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these any further because they have
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different variables they're unlike terms
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all right what if we had 1/2 to 8 minus
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4 B plus 6 on the inside there so again
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I would like to try to simplify
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everything inside of this but they're
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all different a B and then this doesn't
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even have a variable so they're all
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unlike so all I really can do is
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distribute the 1/2 in to each one of
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these things and if you're afraid of
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fractions I'm gonna have to tell you now
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that you're gonna need to get
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comfortable with it so go back to my
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algebra 1 or even in my pre-algebra and
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review fractions because if you don't
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know how to multiply fractions or
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simplify fractions or divide fractions
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then algebra seems hard when it isn't
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hard but you do have to know fractions
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so we're gonna multiply this 1/2 in
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so what we're gonna get when we do that
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is we're gonna have the way I want you
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to write it is don't do everything at
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once write it as 1/2 times 2a you might
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say why am i doing that well it's
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because I want to see what you're doing
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then that's 1/2 times this so it's going
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to be minus 1/2 times 4 B then then I
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have a plus sign from here 1/2 times 6 I
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know that you know that 1/2 times 6 is 3
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but I want to see it as 1/2 times 6 why
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do I want to see it like that because I
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know what you did I don't see any
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simplification I know what you were
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doing and I can see that it makes sense
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now here you have a 2 remember when you
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have that everything's multiplied
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together and so when you have a number
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on the top or a term on the top the same
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as it is on the bottom they can divide
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away 2 divided by 2 is 1 so they strike
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out and they divide from each other or
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they divide out you have a similar thing
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here you have a 4 in a 2 so 2 divided by
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2 is 1 4 divided by 2 is 2 so I can kind
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of like strike that out and put a 2 up
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there 2 divided by 2 is 1 2 2 6 divided
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by 2 is 3 so I can simplify it by kind
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of striking through like that and then
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what I'll get for the answer see once
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this is all done the 2's are gone the 1
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is times a so you just have a for the
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first term the minus sign is still here
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but when you did the strikethrough you
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still had a 2 and you still had a B and
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then everything's gone here except for
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the 3 so you have 3 so this is just
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literally simplifying terms we've
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covered that in algebra 1 over and over
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and over again you should be comfortable
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with simplifying terms this is mostly a
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review so again if you see something
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like this and you're like I have no idea
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why he's strikethrough the top and the
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bottom doesn't make any sense then it
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just means that you've forgotten some
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stuff from algebra 1 so go back to
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algebra 1 go to simplifying expressions
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and what we do tons of cancel a