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

Mathematics
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wow u didn't type @bah here...
I'm not smart enough????

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Other answers:

y=5x+2 y-2 = 5x x = (1/5)(y-2)
10xy + 4y = 10 (1/5)(y-2) y + 4y = 2(y - 2)y + 4y = 2y^2 - 4y + 4y = 2y^2 <-Final answer
and it's you're
o_o I'm taking the PSAT... I don't know how to do these types of questions......
To clarify on what @bahrom7893 said, I would've done something a bit simpler? \[\implies10xy + 4y~~~~~~~~~~Original~Expression\]\[\implies 2y(5x + 2)~~~~~~~~~Factor~out~the~GCF\]\[\implies 2y(y) ~~~~~~~~~~~~~~~~~~Substitute\]\[\implies 2y^2~~~~~~~~~~~~~~~~~~~~~Multiplication~of~variables\]
ok let's do another problem I need to get better.
Uh ok then... \[y = (3x + 2)^3\]\[\text{Simplify in terms of y: } (9x + 6)^3\]
Very similar to the one you were doing on that PSAT question.
ok I think I got it.
so do I multiply to the 3rd power?
Yes, the \(^{'3'}\) implies cubing it or multiplying by itself 3 times.
9x*9x*9x?
Not quite...could you show me what you did?
well you its |dw:1349998059319:dw| so i multiply the exponent to the 3rd?
i know its wrong..
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?
i keep forgetting to factor.....
my spectacles are deceiving me
Hmm?
ok if we can (9x+6) (9x+6) (9x+6)
what's next?
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.
ok will keep it (9x+6)^3
Now factor what's within the parentheses...
3(3x+2)^3
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?
explain those parentheses
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.
oh
\[\LARGE{¿Entiendes?}\]
si
Can you predict what to do next?
distributive
What? Keep in mind the original question and what y is equal to...
then we should substitute
\[\huge\color{red}{Y}\color{blue}{E}\color{salmon}{S}\color{green}{!}\]
so ....
instead of the x make it a y?
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.
jinkies
hmm ummm
y=27x^3+8
Umm...no... \[(9x + 6)^3 \implies (3(3x + 2))^3 \implies 3^3(3x + 2)^3 \implies 27(3x + 2)^3 \implies 27y\]
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?
I still don't get how divided 27(3x+2)^3 to get 27y
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.
where does (3x+2)^3? disappear?
I don't understand the y part...
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
You still there?
im here

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