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morganalana17

  • 3 years ago

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  1. blurbendy
    • 3 years ago
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    I know about Pascal's triangle, but I don't know if that's what you're referring to.

  2. blurbendy
    • 3 years ago
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    Sure, do need an explanation of what it is, or do you have a problem you want me to look at?

  3. blurbendy
    • 3 years ago
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    you*

  4. hba
    • 3 years ago
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    http://mathworld.wolfram.com/PascalsTheorem.html

  5. blurbendy
    • 3 years ago
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    Sure, do you know how to expand a binomial (something)^2?

  6. blurbendy
    • 3 years ago
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    Okay, let's start there then. Say you have something like (x + y)^2 and we want to expand that. You can rewrite (x + y)^2 so that it's like: (x + y)(x + y) Make sense so far?

  7. blurbendy
    • 3 years ago
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    Good, now we're going to multiply the first x in (x + y) to BOTH the (x + y) in the other term to get: x^2 + xy |dw:1358369073609:dw|

  8. blurbendy
    • 3 years ago
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    Make sense?

  9. precal
    • 3 years ago
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    pascal's triangle is use to expand

  10. precal
    • 3 years ago
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    |dw:1358369183479:dw|

  11. blurbendy
    • 3 years ago
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    Great, then we move on and do the same thing with the first y. and get xy + y^2, so in total we have x^2 + xy + xy + y^2

  12. precal
    • 3 years ago
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    |dw:1358369198853:dw|do you see the pattern?

  13. blurbendy
    • 3 years ago
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    @precal, that's what im attempting to show. thanks for the visual though :)

  14. blurbendy
    • 3 years ago
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    perfect, so we have x^2 + xy + xy + y^2 which equals x^2 + 2xy + y^2, which is what precal's picture shows

  15. precal
    • 3 years ago
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    |dw:1358369366989:dw|

  16. precal
    • 3 years ago
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    |dw:1358369387693:dw|then notice what is happening to the x powers and then the y powers

  17. precal
    • 3 years ago
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    x powers start at 2 while y start at 0

  18. precal
    • 3 years ago
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    this is the pattern you will follow for you problem

  19. blurbendy
    • 3 years ago
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    Now, if we wanted to take that further like (x +y)^3 (like your problem) we can do two things.

  20. precal
    • 3 years ago
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    |dw:1358369548166:dw|you will use the 3rd row

  21. precal
    • 3 years ago
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    |dw:1358369588020:dw|

  22. blurbendy
    • 3 years ago
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    We could multiply (x + y)(x^2 + 2xy + y^2) And do the EXACT same thing like how we were multiplying the x to the second term and then the y to the second term.

  23. blurbendy
    • 3 years ago
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    That would give us the correct answer, OR we could use the pattern precal is showing us.

  24. precal
    • 3 years ago
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    |dw:1358369600649:dw|

  25. precal
    • 3 years ago
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    be careful with your second term because of the negative, just simplify and you are done

  26. precal
    • 3 years ago
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    yw

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