Manipulating expressions
Combining like terms Leveraging the power of Chuck Norris to understand combining like terms in expressions
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- Let's say that I've got two Chuck Norrises (or maybe it's Chuck Norri)
- and to that I am going to add another three Chuck Norrises
- So I'm going to add another three Chuck Norrises
- And this might seem a little bit obvious but how many Chuck Norrises do I now have?
- Well, two Chuck Norrises - we can represent this as literally a Chuck Norris plus a Chuck Norris
- So let me do that, a Chuck Norris plus another Chuck Norris - two Chuck Norrises.
- You can also view that as 2 times Chuck Norris and this is just another way of representing it
- And three Chuck Norrises
- You could view that as a Chuck Norris, plus a Chuck Norris, plus another Chuck Norris
- And so we would have a grand total (and this might be very simple for you)
- But you would have a grand total of 1..2..3..4..5 Chuck Norrises
- So this would be equal to
- 5 Chuck Norrises
- Now let's get a little bit more abstract here
- Chuck Norris is a very tangible thing
- So let's go to a little bit more of the traditional algebraic notation.
- If I have two X's
- And remember 2x - you can view this as two X's or two times X.
- And to that I were to add 3 X's
- How many X's do I have?
- Well, once again, 2 X's that's 2 times X and you can view it as an X plus an X.
- We don't know what the value of X is but whatever that value is we can add it to itself
- And then three X's are going to be that value
- I'll do it in that same green colour
- Three X's are going to be that value
- plus that value
- plus whatever that value is
- And so how many X's do I now have?
- Well, I'm going to have 1..2..3..4..5 X's
- So 2x plus 3x is equal to
- 5x
- And if you think about it, all we really did (and hopefully you conceptually get it)
- We just added the two numbers that were multiplying the X.
- And these numbers, the two or the three
- they're called "coefficients"
- Very fancy word - but it's just this constant number, this regular number, that's multiplied by the variable.
- You just added the two and the three to get your 5x.
- Now let's think about this a little bit more
- Let's go back to this original expression, the two Chuck Norrises plus three Chuck Norrises.
- Let's say, to that we were to add
- Let's say we were to add some type of a...
- Let's say we were to add seven plums over here
- So this is my drawing of a plum
- So we have seven plums plus two Chuck Norrises plus three Chuck Norrises
- And let's say that I add another two plums
- I add another two plums here
- So what would this whole thing be?
- Well, I wouldn't add the seven to the two to the three plus the two
- We're adding different things here!
- You have two Chuck Norrises and three Chuck Norrises
- So they're still going to simplify to five Chuck Norrises
- And then we would separately think about the plums
- We have seven plums and we're adding another two plums
- We're going to have nine plums
- Plus nine plums
- So this simplifies to five Chuck Norrises and nine plums
- Similarly, over here, if I had instead of just 2x plus 3x
- If I had 7y
- 7y plus 2x plus 3x plus 2y
- What do I now have?
- Well, I can't add the X's and the Y's
- They could very well represent a different number
- So all I can do is really, add the X's (and then I get the 5x)
- And then I'd separately add the Y's
- If have seven Y's and to that I add two Y's
- I'm going to have nine Y's
- If I have seven of something and I have two of something, I now have nine of that something
- So I'm going to have nine Y's
- So you add that (we'll do that in a different colour)
- You add this
- ... and this
- ... you get that
- You add the X's
- ... you get that right over there
- So hopefully that makes a little sense
- Actually, I'll throw out one more idea
- So given this, what would happen if I were to have
- 2x plus 1 plus 7x plus 5?
- Well, once again, you might be tempted to add the two plus the one
- But they're adding different things!
- These are two X's, this is just the number one
- So you really just have to add the X's together.
- So you're going to say "well I've got two X's
- and I'm going to add seven X's to that"
- Well that means that I now have nine X's
- And then separately, you would say
- "Well, I've got just the abstract number one
- and then I've got another five"
- One plus five is going to be equal to six.
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At 5:31, how is the moon large enough to block the sun? Isn't the sun way larger?
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