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

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saj-94 | (Level 1) Salutatorian

Posted September 3, 2013 at 7:29 AM via web

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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

Posted September 3, 2013 at 7:42 AM (Answer #1)

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`(2-y)^5`

Using binomial theorem;

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

`(2-y)^5=sum_(r=0)^5 ^5C_r 2^r (-1)^(5-r) y^(5-r)`

To get y in ascending order we need to put r from the last to the first.

`T_5 = ^5C_5 2^5 (-1)^5-5 y^(5-5) = 32`

`T_4 = ^5C_4 2^4 (-1)^5-4 y^(5-4) = -80y`

`T_3 = ^5C_3 2^3 (-1)^5-3 y^(5-3) = 80y^2`

So the first three terms in ascending order of y is `32,-80y,80y^2`

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