pokemon23
If y = 5x + 2, then find the value of
10xy + 4y in terms of y.
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pokemon23
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@Hero @Calcmathlete
bahrom7893
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wow u didn't type @bah here...
bahrom7893
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I'm not smart enough????
bahrom7893
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y=5x+2
y-2 = 5x
x = (1/5)(y-2)
bahrom7893
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10xy + 4y = 10 (1/5)(y-2) y + 4y = 2(y - 2)y + 4y = 2y^2 - 4y + 4y = 2y^2 <-Final answer
bahrom7893
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and it's you're
pokemon23
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o_o I'm taking the PSAT... I don't know how to do these types of questions......
Calcmathlete
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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
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ok let's do another problem I need to get better.
Calcmathlete
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Uh ok then...
\[y = (3x + 2)^3\]\[\text{Simplify in terms of y: } (9x + 6)^3\]
Calcmathlete
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Very similar to the one you were doing on that PSAT question.
pokemon23
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ok I think I got it.
pokemon23
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so do I multiply to the 3rd power?
Calcmathlete
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Yes, the \(^{'3'}\) implies cubing it or multiplying by itself 3 times.
pokemon23
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9x*9x*9x?
Calcmathlete
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Not quite...could you show me what you did?
pokemon23
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well you its |dw:1349998059319:dw| so i multiply the exponent to the 3rd?
pokemon23
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i know its wrong..
Calcmathlete
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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
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i keep forgetting to factor.....
pokemon23
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my spectacles are deceiving me
Calcmathlete
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Hmm?
pokemon23
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ok if we can (9x+6) (9x+6) (9x+6)
pokemon23
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what's next?
Calcmathlete
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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
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ok will keep it (9x+6)^3
Calcmathlete
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Now factor what's within the parentheses...
pokemon23
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3(3x+2)^3
Calcmathlete
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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
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explain those parentheses
Calcmathlete
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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
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oh
Calcmathlete
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\[\LARGE{¿Entiendes?}\]
pokemon23
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si
Calcmathlete
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Can you predict what to do next?
pokemon23
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distributive
Calcmathlete
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What? Keep in mind the original question and what y is equal to...
pokemon23
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then we should substitute
Calcmathlete
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\[\huge\color{red}{Y}\color{blue}{E}\color{salmon}{S}\color{green}{!}\]
pokemon23
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so ....
pokemon23
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instead of the x make it a y?
Calcmathlete
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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
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jinkies
pokemon23
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hmm ummm
pokemon23
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y=27x^3+8
Calcmathlete
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Umm...no...
\[(9x + 6)^3 \implies (3(3x + 2))^3 \implies 3^3(3x + 2)^3 \implies 27(3x + 2)^3 \implies 27y\]
Calcmathlete
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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
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I still don't get how divided 27(3x+2)^3 to get 27y
Calcmathlete
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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
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where does (3x+2)^3? disappear?
pokemon23
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I don't understand the y part...
Calcmathlete
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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
Calcmathlete
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You still there?
pokemon23
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im here