How do you use the binomial #(2v+3)^6# using Pascal's triangle?

1 Answer
Apr 9, 2017

Answer:

#64v^6+576v^5+2160v^4+4320v^3+4860v^2+2916v+729#

Explanation:

Expand using the corresponding row of coefficients from Pascal's triangle for n = 6

#rArr1color(white)(xx)6color(white)(xx)15color(white)(xx)20color(white)(xx)15color(white)(xx)6color(white)(xx)1#

with #color(blue)"decreasing powers" " of "2v" from " (2v)^6to(2v)^0#

#"and "color(blue)" increasing powers"" of " 3" from " 3^0to3^6#

#1.(2v)^6. 3^0+6.(2v)^5. 3^1+15.(2v)^4. 3^2+20.(2v)^3. 3^3#

#+15.(2v)^2. 3^4+6.(2v)^1. 3^5+1.(2v)^0. 3^6#

#=64v^6+576v^5+2160v^4+4320v^3+4860v^2+2916v+729#