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

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

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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.


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



`(-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`