Homework Help

Find the first 3 terms in the expansion of (2 − y)^5 in ascending powers of y

user profile pic

roshan-rox | (Level 1) Valedictorian

Posted June 9, 2013 at 2:13 AM via web

dislike 2 like

Find the first 3 terms in the expansion of (2 − y)^5 in ascending powers of y

1 Answer | Add Yours

user profile pic

jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted June 9, 2013 at 2:27 AM (Answer #1)

dislike 1 like

This can be done using binomial expansion. The expression for binomial expansion is given below.

`(a+b)^n = sum_(r = 0)^n^nC_ra^rxxb^(n-r)`

As you can see from the above equation a is ascending and b is descending.

`(2-y)^5`

If we need y in ascending order we have to take y at the initial position.

`(-y+2)^5`

 

`(-y+2)^5 = sum_(r = 0),^5^5C_r(-y)^rxx2^(5-r)`

 

`T_1 = ^5C_0(-y)^0xx2^(5-0) = 32`

`T_2 = ^5C_1(-y)^1xx2^(5-1) = -80y`

`T_3 = ^5C_2(-y)^2xx2^(5-2) = 80y^2`

 

So the first three of the expansion is `32,(-80y),80y^2`

Sources:

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes