## pokemon23 Group Title If y = 5x + 2, then find the value of 10xy + 4y in terms of y. one year ago one year ago

1. pokemon23 Group Title

@Hero @Calcmathlete

2. bahrom7893 Group Title

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

3. bahrom7893 Group Title

I'm not smart enough????

4. bahrom7893 Group Title

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

5. bahrom7893 Group Title

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

6. bahrom7893 Group Title

and it's you're

7. pokemon23 Group Title

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

8. Calcmathlete Group Title

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$

9. pokemon23 Group Title

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

10. Calcmathlete Group Title

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

11. Calcmathlete Group Title

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

12. pokemon23 Group Title

ok I think I got it.

13. pokemon23 Group Title

so do I multiply to the 3rd power?

14. Calcmathlete Group Title

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

15. pokemon23 Group Title

9x*9x*9x?

16. Calcmathlete Group Title

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

17. pokemon23 Group Title

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

18. pokemon23 Group Title

i know its wrong..

19. Calcmathlete Group Title

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?

20. pokemon23 Group Title

i keep forgetting to factor.....

21. pokemon23 Group Title

my spectacles are deceiving me

22. Calcmathlete Group Title

Hmm?

23. pokemon23 Group Title

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

24. pokemon23 Group Title

what's next?

25. Calcmathlete Group Title

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.

26. pokemon23 Group Title

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

27. Calcmathlete Group Title

Now factor what's within the parentheses...

28. pokemon23 Group Title

3(3x+2)^3

29. Calcmathlete Group Title

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?

30. pokemon23 Group Title

explain those parentheses

31. Calcmathlete Group Title

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.

32. pokemon23 Group Title

oh

33. Calcmathlete Group Title

$\LARGE{¿Entiendes?}$

34. pokemon23 Group Title

si

35. Calcmathlete Group Title

Can you predict what to do next?

36. pokemon23 Group Title

distributive

37. Calcmathlete Group Title

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

38. pokemon23 Group Title

then we should substitute

39. Calcmathlete Group Title

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

40. pokemon23 Group Title

so ....

41. pokemon23 Group Title

instead of the x make it a y?

42. Calcmathlete Group Title

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.

43. pokemon23 Group Title

jinkies

44. pokemon23 Group Title

hmm ummm

45. pokemon23 Group Title

y=27x^3+8

46. Calcmathlete Group Title

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

47. Calcmathlete Group Title

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?

48. pokemon23 Group Title

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

49. Calcmathlete Group Title

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.

50. pokemon23 Group Title

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

51. pokemon23 Group Title

I don't understand the y part...

52. Calcmathlete Group Title

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

53. Calcmathlete Group Title

You still there?

54. pokemon23 Group Title

im here