Answer:
32k^5 -80k^4·b +80k^3·b^2 -40k^2·b^3 +10k·b^4 -b^5
Step-by-step explanation:
The relevant row of Pascal's triangle is the one with 5 (the exponent) as the second number. That row is ...
1 5 10 10 5 1
These are the multipliers used for the terms of the expanded sum.
Each term of (a+b)^n is of the form a^(n-j)·b^j for j ranging from 0 to n. It is multiplied by the corresponding term in the row of Pascal's triangle.
(2k -b)^5 = 1(2k)^5(-b)^0 +5(2k)^4(-b)^1 +10(2k)^3(-b)^2 +10(2k)^2(-b)^3 +5(2k)^1(-b)^4 +1(2k)^0(-b)^5
= 32k^5 -80k^4·b +80k^3·b^2 -40k^2·b^3 +10k·b^4 -b^5
