WEBVTT
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All right, we're still working on problems from chapter 1, 1.7.
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Part 1, use the distributive property to write each expression without parentheses, then
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simplify the result if possible.
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So the first problem is 4 times x plus y.
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And so when you do the distributive property, you have to do 4 times x plus 4 times y because
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you remember you're distributing the 4 to each thing in the parentheses.
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And so our answer is just 4x plus 4y.
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I'm not always going to show that middle step that I wanted to begin with that.
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Okay, let's go on to number 2.
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We have 5 times 3x minus 7.
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Similar, 5 times 3x minus 5 times 7.
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So that'll give us 15x minus 35.
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Okay, let's go on to number 3.
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Negative 3 times x plus 10.
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Now let's remember you're distributing the negative 3.
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So negative 3 times x plus negative 3 times 10, which is negative 3x.
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Now this is going to be plus negative 30.
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But the way we want to write that is just minus 30.
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You don't want to write plus the negative.
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You could and then at the next step, right?
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Negative 3x minus 30.
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Let's go to number 4.
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Negative 3 times 2x minus 4.
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Right, very similar, but we've got to be very careful of these negative signs.
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We've got negative 3 times 2x.
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Now, you could think this is plus and negative 3, or you just say minus 3.
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That's the same thing as saying plus and negative 3.
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But you also have this negative 4.
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So it's a little bit confusing.
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So what you're distributing really is you could think of taking the negative 3 and you're
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going to multiply it by the negative 4.
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Okay?
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In any case, we're going to end up with a negative and a negative somehow.
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So then we get negative 6x plus 12.
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Common mistake is to write minus 12, not to use both these negative signs.
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All right, so that's 1 through 4.
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Let's go on to number 5.
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This one can be done two ways.
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You could think of when you have a minus sign out in front of a parentheses, you're just
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going to distribute the minus sign by writing the opposite of everything inside the parentheses.
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So inside the parentheses is an x.
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So the opposite of that will be negative x.
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Next you see a plus 8, the opposite of that will be a minus 8.
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So that's one way to get the answer.
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That's probably the easiest.
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Another way of thinking about this problem is that minus sign out in front could be thought
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of as a negative 1 times x plus 8.
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And then you're going to distribute the negative 1 times x plus negative 1 times 8 to get a
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negative x.
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And notice, this will give you a plus and negative 8.
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I'm going to just write that as minus 8.
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It's more simplified to write minus 8.
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You don't want to ever write a plus and then a minus sign right after it.
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That makes it really confusing.
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All right, let's go on to number 6.
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Similar problem.
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We've got a negative side on the outside and a negative 2x minus 1.
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Let's just do this by taking the opposite of everything inside the parentheses.
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That's how you could think of this minus sign.
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It's the opposite of everything inside.
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So inside is a negative 2x.
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That will become a positive 2x.
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And inside is a negative 1.
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So you're going to change that to a plus 1.
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And that's all there is to it.
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You could do it the second way, like I did at number 5 by distributing a negative 1
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to each thing inside the parentheses.
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And you should get exactly the same answer.
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All right, 7.
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We've got 2 7s times 35x minus 14.
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So you can do this.
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We're going to distribute your 2 7s.
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So you have 2 7s times 35x.
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Now, I'm going to write that 35 as 35 over 1.
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All right.
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So you can cancel easily here minus, and I'm going to get it because from this minus sign,
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I'm going to distribute that 2 7s also to the 14.
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And I'm going to write that as 14 over 1.
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Now, that way it's going to be a little bit easier when we cancel.
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So let's see.
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The 7 goes into the 35 times.
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So what I have here is 2 times 5 over 1 times 1.
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10 over 1 is just 10.
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So this is going to be 10x.
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So you don't want to leave that as 10 over 1.
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And you don't want to leave it as 70 over 7 if you didn't cancel it.
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You have to reduce it all the way down to 10x minus.
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And let's see what's going on over here.
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The 7 goes into the 14 twice.
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So I have 2 times 2 in the numerator over 1 times 1.
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4 over 1 is 4.
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So I've got 10x minus 4.
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All right, one more.
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Number 8, 2 times 3x minus 1 minus negative 20.
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All right.
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So we have a distributed property here, 2 times 3x minus 1.
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Remember the order of operations?
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You do multiplication first.
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Well, first you do inside the parentheses, but they're unlike terms.
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The distributed property is just a way of multiplying
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when you can't simplify inside the parentheses.
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So we're going to have 2 times 3x minus 2 times 1.
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But there's no distributing here.
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This is just saying minus and negative 20.
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This is just dealing with negative numbers, positive and negative numbers.
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So that's going to be plus 20, right?
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Minus and negative, you could write this plus and plus.
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So what do we have here?
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2 times 3x is 6x minus 2 plus 20.
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All right, so we've removed the parentheses,
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but I need to simplify it by adding light terms.
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And these are the two light terms, the negative 2
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and the plus 20.
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So I have to add negative 2 and plus 20.
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That'll be 18.
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So that your final answer is 6x plus 18.