How do you expand # (3a +b)^4 # using Pascal’s Triangle?

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Answer 1 · 2015-08-06T19:52:05

Multiply the #5#th row of Pascal's triangle by a list of descending powers of #3# to find the coefficients of the expansion:

#(3a+b)^4 = 81a^4+108a^3b+54a^2b^2+12ab^3+b^4#

Write down the #5#th row of Pascal's triangle as a sequence:

#1#, #4#, #6#, #4#, #1#

Write down descending powers of #3# from #3^4# to #3^0# as a sequence:

#81#, #27#, #9#, #3#, #1#

Multiply the two sequences together to get:

#81#, #108#, #54#, #12#, #1#

These are the coefficients of the terms in #a^4#, #a^3b#, ... ,#b^4#:

#(3a+b)^4 = 81a^4+108a^3b+54a^2b^2+12ab^3+b^4#

How do you expand # (3a +b)^4 # using Pascal’s Triangle?