How do you use the Binomial Theorem to expand #(2x+3)^3#?

1 Answer
Nov 14, 2016

Answer:

#8x^3 +36x^2+54x+27#

Explanation:

Binomial expansion of #(x+a)^n# is written as follows

= #x^n + nax^(n-1)+ (n(n-1))/(2!) a^2 x^(n-2) +(n(n-1)(n-2))/(3!)a^3 x^(n-3)+......#

To write the binomial expansion of #(2x+3)^3# can be written using the above expression by substituting 2x for x and 3 for a and of course n=3

Accordingly the required expansion would be :
# (2x)^3 +3*3*(2x)^2 +(3*2)/(2!) 3^2 (2x) +(3*2*1)/(3!) 3^3(2x)^0#

=#8x^3 +36x^2+54x+27#