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