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

1 Answer
Sihan Tawsik
Feb 3, 2016

#81a^4-108a^3b+54a^2b^2-12ab^3+b^4#

Explanation:

from pascal's triangle we can see,

#(1+x)^0#---------------------#1#
#(1+x)^1#---------------------#1# #1#
#(1+x)^2#--------------------#1# #2# #1#
#(1+x)^3#--------------------#1# #3# #3# #1#
#(1+x)^4#--------------------#1# #4# #6# #4# #1#

so,
#(3a-b)^4=1*(3a)^4-4*(3a)^3b+6*(3a)^2b^2-4*3ab^3+1*b^4#
#=81a^4-108a^3b+54a^2b^2-12ab^3+b^4#

Related questions
See all questions in Pascal's Triangle and Binomial Expansion
Impact of this question
2131 views around the world
You can reuse this answer
Creative Commons License