Expand the given power by using pascal’s triangle. (2k – b)5

  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

yep

step-by-step explanation:

option 1

data plot with   3 dots over 33, 1 dot over 34, 2 dots over 35, no dot over 36, 1 dot over 37, 2 dots over 38, 4 dots over 39, and 2 dot over 40.