Question 1151220

find the {{{5th}}} term,{{{ (5x+3)^5}}}

use The Binomial Theorem


{{{(5x+3)^5=5C0(5x)^5*3^0+5C1(5x)^4*3^1+5C2(5x)^3*3^2+5C3(5x)^2*3^3+5C4(5x)^1*3^4+5C5(5x)^0*3^5}}}

 the {{{5th}}} term is: {{{5C4(5x)^1*3^4=5*5x*81=2025x}}}


or, you can do it this way:

{{{(5x+3)^5}}}.....expand

{{{(5x+3)^2*(5x+3)^2*(5x+3)}}}

{{{(25x^2 + 30x + 9)*(25x^2 + 30 x + 9)*(5x+3)}}}

{{{(625x^4 + 1500x^3 + 1350x^2 + 540x + 81)*(5x+3)}}}

{{{3125x^5 + 9375x^4 + 11250x^3 + 6750x^2 + 2025x + 243}}}

so, the {{{5th}}} term is {{{2025x}}}