Simplify (-2 x - 9)(-4)can someone help me...No straight answers please...

- anonymous

Simplify (-2 x - 9)(-4)can someone help me...No straight answers please...

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- anonymous

You just have to distribute the multiplication to each term
\[(a + b)(c) = ac + bc\]

- anonymous

Okay....

- anonymous

why adding?

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- anonymous

Why not?

- anonymous

isnt it multiplying? (-2*-9)

- anonymous

So in your case you have (-2x -9)(-4) which is the same as
(-2x + (-9))(-4)

- anonymous

Oh, is that x for multiplication? or is it an x.

- anonymous

i think its multiplying... idk

- anonymous

i think it is just an x

- anonymous

ohh ok

- anonymous

So did that make sense with what you need to do Artist, or do you need a bit more help?

- anonymous

I'm not sure....

- anonymous

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.

- anonymous

So in your case, what is the sum you're multiplying ?

- anonymous

(-2 x - 9)(-4)

- anonymous

Not quite.
(-2x - 9) is a sum.

- anonymous

Specifically it is the sum of -2x and -9

- anonymous

Okay

- anonymous

You know what a sum is right?

- anonymous

Yes...

- anonymous

Tell me =)

- anonymous

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.

- anonymous

Okay.

- anonymous

What is a sum?

- anonymous

A sum is the answer of two numbers added together...

- anonymous

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.

- anonymous

Oh...Okay.

- anonymous

Now then. For each of the sums I listed above, count the number of terms in each sum.

- anonymous

2, then 4?

- anonymous

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.

- anonymous

So how many terms does that last sum have?

- anonymous

*Lightbulb*...Okay...

- anonymous

3?

- anonymous

I am glad I fanned you btw. You've been the best student I've seen here in a long time.

- anonymous

Yes, it has 3.

- anonymous

Really?

- anonymous

Yes.

- anonymous

I'm the best?

- anonymous

So far ;)

- anonymous

Cool...

- anonymous

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.

- anonymous

okay...

- anonymous

So lets look at your problem again.

- anonymous

(-2x - 9)(-4)
What is the sum, and what is k?

- anonymous

the sum is (-2x-9)?

- anonymous

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?

- anonymous

Can you rewrite subtraction as adding a negative?

- anonymous

no...?

- anonymous

2-9 = 2+(-9)
-7 = -7
Right?

- anonymous

Yes.

- anonymous

So do the same thing to the subtraction you have in your sum

- anonymous

I like my sums to only have addition.

- anonymous

feels neater ;p

- anonymous

Yeah...

- anonymous

so, -2x + (- 9,) ?

- anonymous

Yes.

- anonymous

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

- anonymous

So what do you get?

- anonymous

-4*-2+ -4*-9?

- anonymous

Close. Don't forget your x.

- anonymous

8x + 36

- anonymous

like that?

- anonymous

Yes, exactly.

- anonymous

:)

- anonymous

Nice work!

- anonymous

Thank you!

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