Using an example note that #a^0=1# Raise a value to the power of 0 and the answer is 1. So #d^0=1#
You need to use the line for #x^7#
For ease of demonstration set #(d+a)^7->(d+6)^7#
Step 1: Copying the line for #x^7#
#color(white)("d")->1 + 7+21+35+35+21+7+1#
Step 2: Dealing with # color(red)(d) #
#color(white)("d")->1color(red)(d^7) + 7color(red)(d^6)+21color(red)(d^5)+35color(red)(d^4)+35color(red)(d^3)+21color(red)(d^2)+7color(red)(d^1)+1color(red)(d^0)#
Step 3: Dealing with # color(blue)(a) # (which really is 6)
#color(white)("d")->1d^7color(blue)(a^0) + 7d^6color(blue)(a^1)+21d^5color(blue)(a^2)+35d^4color(blue)(a^3)+35d^3color(blue)(a^4)+21d^2color(blue)(a^5)+7d^1color(blue)(a^6)+1d^0color(blue)(a^7)#
See the way the powers of #d# go down as you read left to right. Also note the way the powers of #a# go up as you read left to right.
Substituting for #a=6#
#d^7 + 7d^6 6+21d^5 6^2+35d^4 6^3+35d^3 6^4+21d^2 6^5+7d^1 6^6+6^7#
#color(white)()#
#color(white)()#
#d^7 + 42d^6+756d^5+7560d^4+45360d^3+163296d^2+326592d+279936#
