Question 928075
1.

Each line is also the powers (exponents) of {{{x}}}:

  {{{(3x)^0}}}={{{1}}} (the first line is just a "{{{1}}}")
  {{{ (3x)^1}}}={{{1}}}  {{{1}}} (the second line is "{{{1}}}" and "{{{1}}}")
  {{{(3x)^2}}}={{{1}}}  {{{2}}}  {{{1}}} (the third line is "{{{1}}}", "{{{2}}}", "{{{1}}}")
 {{{ (3x)^3}}}={{{1}}}  {{{3}}}  {{{3}}}  {{{1}}} (the fourth line is "{{{1}}}", "{{{3}}}", "{{{3}}}","{{{1}}}") ...this line is your line

so, {{{(3x+2y)^3 }}} will be:


{{{1* (3x)^3+3*(3x)^2(2y)+3*(3x)(2y)^2+1*(2y)^3}}}

{{{27x^3+3*9*2x^2y+3*3*4xy^2+8y^3}}}

{{{27x^3+54x^2y+36xy^2+8y^3}}}



2.

{{{(x + (2/x))^5}}}


  {{{(x)^0}}}={{{1}}} (the first line is just a "{{{1}}}")
  {{{ (x)^1}}}={{{1}}}  {{{1}}} (the second line is "{{{1}}}" and "{{{1}}}")
  {{{(x)^2}}}={{{1}}}  {{{2}}}  {{{1}}} (the third line is "{{{1}}}", "{{{2}}}", "{{{1}}}")
 {{{ (x)^3}}}={{{1}}}  {{{3}}}  {{{3}}}  {{{1}}} (the fourth line is "{{{1}}}", "{{{3}}}", "{{{3}}}","{{{1}}}") 
 
{{{ (x)^4}}}={{{1}}}  {{{4}}}  {{{6}}}  {{{4}}}  {{{1}}}...the 5th line


{{{ (x)^5}}}={{{1}}}  {{{5}}}  {{{10}}}  {{{10}}}  {{{5}}}  {{{1}}}...the 6th line-your line

{{{1*x^5+5*x^4(2/x)+10x^3(2/x)^2+10x^2(2/x)^3+5x(2/x)^4+(2/x)^5}}}

{{{x^5+10*(x^4/x)+10x^3(4/x^2)+10x^2(8/x^3)+5x(16/x^4)+32/x^5}}}


{{{x^5+10x^3+40x+80/x+80/x^3+32/x^5}}}


{{{x^5+32/x^5+10x^3+80/x^3+40x}}}