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anonymous

  • one year ago

Use the Binomial Theorem to expand the binomial and express the result in simplified form. (5x-5y)3

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  1. anonymous
    • one year ago
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    Help much appreciated!

  2. Nnesha
    • one year ago
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    \[\huge\rm (a+b)^3=1a^3+3a^2b+3ab^2+b^3\]

  3. Nnesha
    • one year ago
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    you can use pascal's triangle for the coefficient and the exponent of first term start from highest degree to 0 and the exponent of 2nd term start from 0 to highest degree |dw:1443580070541:dw| like in this example power of first term is decreasing and 2nd term exponents are increasing

  4. Nnesha
    • one year ago
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    make sense or no ???

  5. anonymous
    • one year ago
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    \[15z-15y?\]

  6. Nnesha
    • one year ago
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    the numbers in red color r from the pascal's triangle|dw:1443580345523:dw| 3rd row

  7. anonymous
    • one year ago
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    So in this case, you would use the third row of pascal's triangle? Since it's to the third power?

  8. Nnesha
    • one year ago
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    yes right

  9. Nnesha
    • one year ago
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    but remember it starts from 0 |dw:1443580628444:dw|

  10. Nnesha
    • one year ago
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    an y question ? can u solve ur question nw ??

  11. anonymous
    • one year ago
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    I'm still kind of confused... do you multiply the coefficients of the binomial's terms (that are being raised to a certain power), by the numbers of the specified Pascal's Triangle row?

  12. Nnesha
    • one year ago
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    yes in ur question there are numbers in first and term so you should multiply the coefficient by the coefficient of the term |dw:1443581219197:dw| now u should multiply the coefficient one by 5^3

  13. Nnesha
    • one year ago
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    \[\large \rm (5x-5y)^3=\color{ReD}{1}(5x)^\color{blue}{3}(-5y)^0+\color{reD}{3}(5x)^\color{blue}{2}(-5y)^1.......+\] as u can see power of first term is decreasing andexponent of 2nd terms is increasing

  14. Nnesha
    • one year ago
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    -3(5x)^2(-5y)^1 = ????

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