Question

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

Answer 1

`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`