How do I use Pascal's triangle to expand #(3a + b)^4#?

Question

9239 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-07-03T22:24:27

Combine a row of Pascal's triangle with a list of powers of #3# to find:

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

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

#1, 4, 6, 4, 1#

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

#81, 27, 9, 3, 1#

Multiply the two sequences together to get the sequence:

#81, 108, 54, 12, 1#

These are the coefficients of the expansion:

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