Given the following statements: $ 2x + 3y =12 $
$ xy = 6$
What is $8x^3 + 27y^3$?

Question

Given the following statements: $ 2x + 3y =12 $
 $ xy = 6$
 What is $8x^3 + 27y^3$?

lgbasallote · Answer

$$(8x^3 + 27y^3) \implies (2x +3y)(4x^2 + 6(xy) + 9y^2$$
does that give you a hint

anonymous · Answer

$$a^3 + b^3 = (a + b)(a^2 + b^2 - ab)$$

parthkohli · Answer

Ah! Gotcha!

apoorvk · Answer

$$8x^3 + 27y^3 = (2x)^3 + (3y)^3$$

Use the funda below:
$$(a)^3+(b)^3 = (a+b)(a^2-ab +b^2)$$

lgbasallote · Answer

$$\implies (2x+3y)[(2x + 3y)^2 - 6(xy)]$$
$$\implies (12)[(12)^2 - 6(6)]$$
$$\implies (12)[144 - 36]$$
etc.

parthkohli · Answer

Yep. Thanks!

mathslover · Answer

@ParthKohli  may i give you an advise?

parthkohli · Answer

Yes, please :)

mathslover · Answer

dude this is in class IX maths 2nd chapter 

try to do problems also from entrancei.com or from ncert exempler problems 

usually this advice is not given by any teacher ( some are exceptional ) but i am giving you since talent needs guidance

:)

parthkohli · Answer

Let me try to watch some videos related to this topic so I could brush-up my skills. Thanks!

mathslover · Answer

Yes that is a better way @ParthKohli but videos are ok for you as you are in a lower age for this level that is you are doing higher but remember : 

when you come in 9th dont prefer videos since videos make the student dependent .. :) 

best of luck dude .. and thanks for taking that as positive

parthkohli · Answer

I disagree: Videos are pretty dynamic and visual.

mathslover · Answer

friend ... they are dynamic and visual , they can be used for at the last days of exams .. to just revise withing minutes 

but my main point was that "dont' dedicate yourself completely on videos .. but since you are at present doing higher .. prefer videos first :) "

parthkohli · Answer

I see. I do know polynomials, but I don't know how to do these kinds of problems. Let me see.

mathslover · Answer

being disagreed has the reason since at this time videos are helping you very much ... for higher level .. .

parthkohli · Answer

I use http://tutorial.math.lamar.edu, but it doesn't have such practice problems.

mathslover · Answer

for practice problems prefer this link : http://www.ncert.nic.in/NCERTS/textbook/textbook.htm?ieep2=2-17

mathslover · Answer

main concepts .. then problems

parthkohli · Answer

I actually do know all these identities, but sometimes it becomes a pain-in-the-brain to apply them.

mathslover · Answer

Hmn yes it becomes .. 

see whenever you are given with that type of questions and you know that is something related to this topic then : try to make it similar to the identities