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anonymous

  • 5 years ago

Find the specified nth term in the expansion of the binomial. (Write the expansion in descending powers of x.) (x - 4y)^6, n = 3

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  1. amistre64
    • 5 years ago
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    1,6,15,20,15,6,1

  2. anonymous
    • 5 years ago
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    Ok so that's from pascal's triangle right... I sort of understand this but still a little confussed

  3. amistre64
    • 5 years ago
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    1x^6 +6x^5y15x^4y20x^3y25x^2y6xy +y yes

  4. anonymous
    • 5 years ago
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    Ok so when I did this I was close but I mixed up the x and y components like x goes down and y goes up...?

  5. amistre64
    • 5 years ago
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    1x^6 +6x^5(-4y) +15x^4(-4y)^2 +20x^3(-4y)^3 +15x^2(-4y)^4 +6x(-4)^5 +(-4)y^6

  6. amistre64
    • 5 years ago
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    yes; the x descends as the y ascends

  7. anonymous
    • 5 years ago
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    just follow wat amistre says

  8. amistre64
    • 5 years ago
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    the 3rd term is: 15(16) x^4 y^2 right?

  9. amistre64
    • 5 years ago
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    lol..... unless we are heading for a cliff, then dont ;)

  10. anonymous
    • 5 years ago
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    lol ok can you explain where you are getting the third term after I fixed my x and y's and combined terms I got 6x(-4)^5 +(-4)y^6....what did you do from there?

  11. amistre64
    • 5 years ago
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    the 'y' component here is (-4y)

  12. amistre64
    • 5 years ago
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    1,6,15...the coeff is gonna be 15 as a standard..

  13. anonymous
    • 5 years ago
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    right...

  14. amistre64
    • 5 years ago
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    x^6,5,4... y^0,1,2 15x^4 (-4y)^2

  15. anonymous
    • 5 years ago
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    oh I see where you got that so if I simplified it it would be 240x^4y^2

  16. amistre64
    • 5 years ago
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    yes :)

  17. anonymous
    • 5 years ago
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    Thank you so much! This was a problem I sat here and was like what the heck am I doing wrong! lol thank you thank you thank you!

  18. amistre64
    • 5 years ago
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    just a moment of lucidity for me :)

  19. anonymous
    • 5 years ago
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    Ha ha brilliant! lol

  20. anonymous
    • 5 years ago
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    ok so I have (x - 2y)^12, n = 6 1, 12, 66,220,495,792, 924,792,495,220,66,12,1 1x^12+12x^11y+66x^10y+220x^9y+495x^8y+792x^7y+924x^6y+792x^5y+495x^4y+495x^3y+220x^2y+66x^1y+12xy+1x

  21. anonymous
    • 5 years ago
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    Idk if I did that right actually...?

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