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

the required function is .

step-by-step explanation:

from the given table it is noticed that the graph passing through (-3,7), (0,4), (3,1) and (8,-4).

it is a linear function because the value of y is decrease by one as the value of x increase by 1.

the slope of the function is

the slope of the function is -1 and the y-intercept is 4.

the slope intercept form is

where, m is slope and b is y-intercept.

therefore the required function is . the graph of this function is shown below.

w'x is 0.

hope it