How do you expand #(3x+2)^3# using Pascal’s Triangle?
1 Answer
Feb 8, 2016
# 27x^3 + 54x^2 + 36x + 8#
Explanation:
From Pascal's Triangle
using row with coefficients : 1 3 3 1
with decreasing powers of 3x from
# (3x)^3 color(black)(" to ") (3x)^0# and increasing powers of 2 from
#(2)^0color(black)(" to ") (2)^3#
#(3x + 2 )^3 = 1.(3x)^3.(2)^0 + 3.(3x)^2.(2)^1 + 3.(3x)^1.(2)^2 + 1.(3x)^0.(2)^3 #
# = 1.(27x^3).1 + 3.(9x^2).2 + 3.(3x).4 + 1.1.8 #
# = 27x^3 + 54x^2 + 36x + 8 #
