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ParthKohli

  • 2 years ago

Factor.

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  1. ParthKohli
    • 2 years ago
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  2. ParthKohli
    • 2 years ago
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    I know this simplifies to\[\left(\dfrac{2}{3}x + \dfrac{5}{3}y\right)^3 + \rm blah\]

  3. ParthKohli
    • 2 years ago
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    So for the first two terms, should I use \(a^3 + b^3 = (a + b)(a^2 - ab + b^2)\)?

  4. ParthKohli
    • 2 years ago
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    That'd make stuff very long.

  5. hartnn
    • 2 years ago
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    its like \((a+b)^3+(c-b)^3-(a+c)^3\)

  6. ParthKohli
    • 2 years ago
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    Yeah. :-|

  7. ParthKohli
    • 2 years ago
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    Wait, so\[(a + c)(a^2 + 2ab + b^2 - (a+b)(c -b) + c^2 - 2cb + b^2) - (a + c)^3\]

  8. hartnn
    • 2 years ago
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    \(\large = 3(a+b)(a+c)(b-c)\)

  9. ParthKohli
    • 2 years ago
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    How did you get that?

  10. ParthKohli
    • 2 years ago
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    It's correct, but is it some sort of identity taught?

  11. hartnn
    • 2 years ago
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    ok, first take last 2 terms, (c-b)^3-(a+c)^3 = ... ? use A^3-B^3 =...

  12. hartnn
    • 2 years ago
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    not identity, you need to work that out...

  13. hartnn
    • 2 years ago
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    its quite long though

  14. ParthKohli
    • 2 years ago
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    \[a^3 - b^3 = (a - b)(a^2 + ab + b^2)\]So here,\[= -(b +a)(\cdots)\]Err

  15. ParthKohli
    • 2 years ago
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    No shortcuts?

  16. hartnn
    • 2 years ago
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    none that i can think of.

  17. ParthKohli
    • 2 years ago
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    There's always a shortcut in exam questions. It's not like an Olympiad one.

  18. hartnn
    • 2 years ago
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    then you must be having choices ?

  19. ParthKohli
    • 2 years ago
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    No choices given. That's all.

  20. ParthKohli
    • 2 years ago
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    :-(

  21. hartnn
    • 2 years ago
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    then i'll wait for someone to suggest a shortcut.....

  22. ParthKohli
    • 2 years ago
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    OK, thanks for the support :-)

  23. some_someone
    • 2 years ago
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    Is Pascal's Triangle any useful? http://www.mathsisfun.com/pascals-triangle.html

  24. some_someone
    • 2 years ago
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    I usually use that, but i don't know if its going to help you?

  25. ParthKohli
    • 2 years ago
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    @hartnn Oh BTW, I found the solution.

  26. hartnn
    • 2 years ago
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    any shortcuts ?

  27. hartnn
    • 2 years ago
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    isn't that exactly what i told you ?

  28. ParthKohli
    • 2 years ago
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    :-P

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