Find underset(r=0) overset(10)sumr^ (10)...

Find `underset(r=0) overset(10)sumr^ (10)C_(r).3^(r).(-2)^(10-r)`

300

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The correct Answer is:

`underset(r=0)overset(10)sumr^(10)C_(r)3^(r)(-2)^(10-r)= 10 underset(r=0)overset(10)sum.^(9)C_(r-1)3^(r)(-2)^(10-r)`
`= 10 xx 3 underset(r=0)overset(10)sum.^(9)C_(r-1)3^(r-1)(-2)^(10-r)`
`= 30(3-2)^(9) = 30`

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