How to solve (5x+3y)^5

Question

How do i solve (5x+3y)^5 using binomial expansion? I get how to do (x+y)^n (n= any positive integer) by using pascal's triangle, but im not getting how to add coefficients of the variables.

Answer 1

(5x + 3y)^5

the sixth row of pascal's triangle gives us

1,5,10,10,5,1

so without the coefficients it would be

x^5 + 5x^4 y + 10x^3 y^2 + 10x^2 y^3 + 5x y^4 + y^5

now on each term add the coefficients on each x add 5^x and same for y 3^y

5^5x^5 +5(5^4)(3)x^4 y + 10(5^3)(3^2)x^3 y^2 +

  10(5^2)(3^3)x^2 y^3 + 5(5)(3^4)x y^4 + 3^5 y ^5