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March 26, 2017

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Expand (2x+5y)^6

  • Math - ,

    The binomial coefficients for (a+b)^6 are:
    1 6 15 20 15 6 1
    which translates to:
    (a+b)^6
    =a^6 + 6a^5b + 15a^4b^2 + 20a^3b^3 + 15 a^2b^4 + 6 ab^5 + b^6

    Substitute a=2x, b=5y into the expansion to get the expansion of
    (2x+5y)^6 accordingly.

  • Math - ,

    Pascal triangle:
    1
    1 1
    1 2 1
    1 3 3 1
    1 4 6 4 1
    1 5 10 10 5 1
    1 6 15 20 15 6 1<-


    (2x+5y)^6=(2x)^6+6(2x)^5(5y)+15(2x)^4(5y)^2+20(2x)^3(5y)^3+15(2x)^2(5y)^4+6(2x)(5y)^5+
    (5y)^6

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