Posted by Megan on Thursday, May 12, 2011 at 5:14pm.
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.
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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