## pokemon23 3 years ago If y = 5x + 2, then find the value of 10xy + 4y in terms of y.

1. pokemon23

@Hero @Calcmathlete

2. bahrom7893

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

3. bahrom7893

I'm not smart enough????

4. bahrom7893

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

5. bahrom7893

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

6. bahrom7893

and it's you're

7. pokemon23

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

8. Calcmathlete

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

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

10. Calcmathlete

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

11. Calcmathlete

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

12. pokemon23

ok I think I got it.

13. pokemon23

so do I multiply to the 3rd power?

14. Calcmathlete

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

15. pokemon23

9x*9x*9x?

16. Calcmathlete

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

17. pokemon23

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

18. pokemon23

i know its wrong..

19. Calcmathlete

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

i keep forgetting to factor.....

21. pokemon23

my spectacles are deceiving me

22. Calcmathlete

Hmm?

23. pokemon23

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

24. pokemon23

what's next?

25. Calcmathlete

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

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

27. Calcmathlete

Now factor what's within the parentheses...

28. pokemon23

3(3x+2)^3

29. Calcmathlete

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

explain those parentheses

31. Calcmathlete

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

oh

33. Calcmathlete

$\LARGE{¿Entiendes?}$

34. pokemon23

si

35. Calcmathlete

Can you predict what to do next?

36. pokemon23

distributive

37. Calcmathlete

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

38. pokemon23

then we should substitute

39. Calcmathlete

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

40. pokemon23

so ....

41. pokemon23

instead of the x make it a y?

42. Calcmathlete

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

jinkies

44. pokemon23

hmm ummm

45. pokemon23

y=27x^3+8

46. Calcmathlete

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

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

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

49. Calcmathlete

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

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

51. pokemon23

I don't understand the y part...

52. Calcmathlete

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

You still there?

54. pokemon23

im here