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

1 Answer
Jul 3, 2015

Answer:

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#

Explanation:

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#