How do you use the binomial series to expand #(3a+4b)^4#?

1 Answer
Feb 26, 2017

Answer:

#81a^4 +432ba^3 +864b^2a^2 +768b^3 a+256b^4#

Explanation:

Binomial expansion of #(x+a)^n=x^n +nC1 ax^(n-1) +nC2 a^2x^(n-2) +.....#

Now use n=4, x= 3a , a =4b and write the expansion

#(3a+4b)^4= (3a)^4 +4C1 (4b) (3a)^3 + 4C2 (4b)^2 (3a)^2 +4C3 (4b)^3 (3a) + 4C4 (4b)^4#

=#81a^4 +432ba^3 +864b^2a^2 +768b^3 a+256b^4#

[4C1=4; 4C2=#(4.3)/(1.2)=6#; 4C3=#(4.3.2)/(1.2.3)=4;

4C4=#(4.3.2.1)/(1.2.3.4)=1#]