Originally Posted by
skeeter the coefficients of the expanded form of $\displaystyle (x+y)^5$ are contained in the 6th row of Pascal's triangle ...
1 , 5 , 10 , 10 , 5 , 1
$\displaystyle (x+y)^5 = x^5 + 5x^4y + 10x^3y^2 + 10x^2y^3 + 5xy^4 + y^5
$
note that the exponents of $\displaystyle x$ start at 5 and decrease to 0 ... and the exponents of $\displaystyle y$ start at 0 and increase to 5.
now, replace $\displaystyle x$ with $\displaystyle a$ and $\displaystyle y$ with $\displaystyle (-3b)$
$\displaystyle (a-3b)^5 = a^5 + 5a^4(-3b) + 10a^3(-3b)^2 ...$ and so on