Question 1185340
<pre>
Every term of {{{(a+b)^n}}} is of the form {{{(matrix(2,1,n,r))a^r*b^(n-r)}}}

Therefore, every term of {{{(x^2+3x)^15}}} is of the form

{{{(matrix(2,1,15,r))(x^2)^r*(3x)^(15-r)}}}

{{{(matrix(2,1,15,r))x^(2r)*3^(15-r)*x^(15-r)}}}

{{{(matrix(2,1,15,r))*3^(15-r)x^(15+r)}}}

We want the exponent of x to be 27, so we set

15+r = 27
   r = 12

{{{(matrix(2,1,15,12))*3^(15-12)x^(15+12)}}}

{{{455*3^(3)x^(27)}}}

{{{455*27x^(27)}}}

{{{12285x^(27)}}}

Its coefficient is 12285

Edwin</pre>