If y = 5x + 2, then find the value of
10xy + 4y in terms of y.

- pokemon23

If y = 5x + 2, then find the value of
10xy + 4y in terms of y.

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- pokemon23

@Hero @Calcmathlete

- bahrom7893

wow u didn't type @bah here...

- bahrom7893

I'm not smart enough????

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## More answers

- bahrom7893

y=5x+2
y-2 = 5x
x = (1/5)(y-2)

- bahrom7893

10xy + 4y = 10 (1/5)(y-2) y + 4y = 2(y - 2)y + 4y = 2y^2 - 4y + 4y = 2y^2 <-Final answer

- bahrom7893

and it's you're

- pokemon23

o_o I'm taking the PSAT... I don't know how to do these types of questions......

- anonymous

To clarify on what @bahrom7893 said, I would've done something a bit simpler? \[\implies10xy + 4y~~~~~~~~~~Original~Expression\]\[\implies 2y(5x + 2)~~~~~~~~~Factor~out~the~GCF\]\[\implies 2y(y) ~~~~~~~~~~~~~~~~~~Substitute\]\[\implies 2y^2~~~~~~~~~~~~~~~~~~~~~Multiplication~of~variables\]

- pokemon23

ok let's do another problem I need to get better.

- anonymous

Uh ok then...
\[y = (3x + 2)^3\]\[\text{Simplify in terms of y: } (9x + 6)^3\]

- anonymous

Very similar to the one you were doing on that PSAT question.

- pokemon23

ok I think I got it.

- pokemon23

so do I multiply to the 3rd power?

- anonymous

Yes, the \(^{'3'}\) implies cubing it or multiplying by itself 3 times.

- pokemon23

9x*9x*9x?

- anonymous

Not quite...could you show me what you did?

- pokemon23

well you its |dw:1349998059319:dw| so i multiply the exponent to the 3rd?

- pokemon23

i know its wrong..

- anonymous

If you were to actually multiply it out, it would be like doing this:
\[(9x + 6)^3 \implies (9x + 6)(9x + 6)(9x + 6)\]which is unnecessary here. Again, like previous times, do you see anything that you can factor out?

- pokemon23

i keep forgetting to factor.....

- pokemon23

my spectacles are deceiving me

- anonymous

Hmm?

- pokemon23

ok if we can (9x+6) (9x+6) (9x+6)

- pokemon23

what's next?

- anonymous

THat is not a step that we even need to take, but we can solve it using that. It would be a slightly longer process though. Let's work WITHIN the parentheses first. Don't do anything ith the \(^3\) for now.

- pokemon23

ok will keep it (9x+6)^3

- anonymous

Now factor what's within the parentheses...

- pokemon23

3(3x+2)^3

- anonymous

The 3 wouldn't go outside of the parentheses because it's still under the \(^3\), so it would become \((3(3x + 2))^3\) Do you see why that is?

- pokemon23

explain those parentheses

- anonymous

Well, let's take the approach that you had before.
\[(9x + 6)^3 \implies (9x + 6)(9x + 6)(9x + 6) \implies 3(3x + 2)3(3x + 2)3(3x + 2)\]\[3 \times 3 \times 3(3x + 2)(3x + 2)(3x + 2) \implies 3^3(3x + 2)^3~~~OR~~~27(3x + 2)^3\]See what I did? You can't take the 3 \(\LARGE{ENTIRELY}\) out of the parentheses unless you take the \(^3\) with it.

- pokemon23

oh

- anonymous

\[\LARGE{¿Entiendes?}\]

- pokemon23

si

- anonymous

Can you predict what to do next?

- pokemon23

distributive

- anonymous

What? Keep in mind the original question and what y is equal to...

- pokemon23

then we should substitute

- anonymous

\[\huge\color{red}{Y}\color{blue}{E}\color{salmon}{S}\color{green}{!}\]

- pokemon23

so ....

- pokemon23

instead of the x make it a y?

- anonymous

Uh...remember that \(y = (3x + 2)^3...\) You can substitute y in for that value now. Tell me what your final answer would be now.

- pokemon23

jinkies

- pokemon23

hmm ummm

- pokemon23

y=27x^3+8

- anonymous

Umm...no...
\[(9x + 6)^3 \implies (3(3x + 2))^3 \implies 3^3(3x + 2)^3 \implies 27(3x + 2)^3 \implies 27y\]

- anonymous

Do you see why? Do you understand what it means when it says "in terms of y"? Do you see that we're replacing ALL OF \((3x + 2)^3\) with y? That way nothing in that is cubed anymore?

- pokemon23

I still don't get how divided 27(3x+2)^3 to get 27y

- anonymous

Where do you see a division symbol? There is no division invloved in this except the beginning factoring portion.
\[\large{\text{We just clarified that y}}~\LARGE\text{=}~\large{(3x + 2)^3}\]Just replace \((3x + 2)^3\) with y and that's all that happened.

- pokemon23

where does (3x+2)^3? disappear?

- pokemon23

I don't understand the y part...

- anonymous

fdiofvejbvnweokgnweoifnerwo That is what we're substituting with y! Remember when we said y = 2 and we plugged it in? Well we could say that 2 = y and we plug y in for the 2. SAME THING HERE.
y = (3x + 2)^3
(3x + 2)^3 = y
Now you just plug in why for the (3x + 2)^3

- anonymous

You still there?

- pokemon23

im here

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