How do you expand #(d + 5)^7# using Pascal’s Triangle?

1 Answer
Aug 17, 2015

You take the seventh row of Pascal's triangle (remember, the 1 at the top counts as row 0)

Explanation:

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In case of #(a+b)^7# the expansion goes like:

#1*a^7*b^0+7*a^6*b^1+21*a^5*b^2..... 7*a^1*b^6+1*a^0*b^7#

The exponents of the first run down from #7->0# and the ones of the other go up from #0->7#. They add up to #7# all the time.

In your case this would be:

#1*d^7*5^0+7*d^6*5^1+21*d^5*5^2+35*d^4*5^3...# and so on
untill #1*d^0*5^7#

#=d^7+35d^6+525d^5...# etc.