SOLUTION: Hello I need help : Use the binomial theorem to write the binomial expansion. (2x+5)^5. I don't understand how to do this.

Hi

In General: (a+b)^n =  where nCk = 

It is relatively easy to understand the expansion in terms of variable's exponents

the coefficients very do-able, once one understands how nCk works with the

denominator canceling out a great deal of the numerator.

5C0 = 5!/0!5! = 1  5C1 = 5!/1!4! = 5  5C2 = 5!/2!3! = 10 etc

(2x+5)^5 =  1a^5 +   5a^4b    + 10a^3b^2     + 10a^2b^3 +     5ab^4 +    1b^5

          5C0       5C1        5C2            5C3            5C4        5C5

(2x +5)^5=  (2x)^5 + 5(2x)^4*5 + 10(2x)^3*25 + 10(2x)^2*125 + 5(2x)*625 + 3125

  Will leave the arithmetic up to Your Calculator