*_Artist_*
Simplify (-2 x - 9)(-4)can someone help me...No straight answers please...
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polpak
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You just have to distribute the multiplication to each term
\[(a + b)(c) = ac + bc\]
*_Artist_*
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Okay....
daria-m
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why adding?
polpak
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Why not?
daria-m
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isnt it multiplying? (-2*-9)
polpak
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So in your case you have (-2x -9)(-4) which is the same as
(-2x + (-9))(-4)
polpak
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Oh, is that x for multiplication? or is it an x.
daria-m
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i think its multiplying... idk
*_Artist_*
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i think it is just an x
daria-m
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ohh ok
polpak
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So did that make sense with what you need to do Artist, or do you need a bit more help?
*_Artist_*
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I'm not sure....
polpak
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Ok lets try this. When you multiply a sum (a + b + c+ ...) by a number k. You simply multiply each of the terms in the sum by that same number k.
polpak
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So in your case, what is the sum you're multiplying ?
*_Artist_*
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(-2 x - 9)(-4)
polpak
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Not quite.
(-2x - 9) is a sum.
polpak
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Specifically it is the sum of -2x and -9
*_Artist_*
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Okay
polpak
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You know what a sum is right?
*_Artist_*
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Yes...
polpak
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Tell me =)
polpak
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One of the most important things to learn in math is the vocabulary. Otherwise it is very difficult to understand what we are talking about if we aren't using the same words for things.
*_Artist_*
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Okay.
polpak
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What is a sum?
*_Artist_*
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A sum is the answer of two numbers added together...
polpak
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Close. Actually a sum is a sequence of terms added together.
2 is not a sum.
2 + 3 is a sum.
2*5 is not a sum.
2+3 + 2*5 is a sum.
*_Artist_*
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Oh...Okay.
polpak
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Now then. For each of the sums I listed above, count the number of terms in each sum.
*_Artist_*
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2, then 4?
polpak
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Close. But notice that the 2 is not being added to the 5, it's multiplied. The terms of a sum are _ONLY_ the things being added together.
polpak
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So how many terms does that last sum have?
*_Artist_*
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*Lightbulb*...Okay...
*_Artist_*
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3?
polpak
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I am glad I fanned you btw. You've been the best student I've seen here in a long time.
polpak
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Yes, it has 3.
*_Artist_*
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Really?
polpak
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Yes.
*_Artist_*
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I'm the best?
polpak
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So far ;)
*_Artist_*
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Cool...
polpak
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Ok so now. Going back to what I was saying before.. If you have a number k multiplied by a sum. You simply distribute the multiplication of k to each term in the sum.
*_Artist_*
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okay...
polpak
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So lets look at your problem again.
polpak
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(-2x - 9)(-4)
What is the sum, and what is k?
*_Artist_*
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the sum is (-2x-9)?
polpak
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Yes!. But I get confused easily, so can you rewrite that as an equivalent sum (equals the same thing) so that it is explicitly two terms being _ADDED_ together?
polpak
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Can you rewrite subtraction as adding a negative?
*_Artist_*
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no...?
polpak
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2-9 = 2+(-9)
-7 = -7
Right?
*_Artist_*
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Yes.
polpak
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So do the same thing to the subtraction you have in your sum
polpak
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I like my sums to only have addition.
polpak
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feels neater ;p
*_Artist_*
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Yeah...
*_Artist_*
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so, -2x + (- 9,) ?
polpak
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Yes.
polpak
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So now you have this sum (-2x + -9) and you're
multiplying it by (-4). So to do that you just multiply
each term in the sum by the -4.
(a + b)(c) = a*c + b*c
polpak
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So what do you get?
*_Artist_*
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-4*-2+ -4*-9?
polpak
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Close. Don't forget your x.
*_Artist_*
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8x + 36
*_Artist_*
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like that?
polpak
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Yes, exactly.
*_Artist_*
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:)
polpak
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Nice work!
*_Artist_*
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Thank you!