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Using binomial theorem, write down the e...

Using binomial theorem, write down the expansions of the following: `(2x+3y)^5`

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`(2x+y)^(5)`
`=overset(5)underset(r=0)(Sigma).^(5)C_(r)(2x)^(5-r).y^(r)`
`=.^(5)C_(0)(2x)^(5)+^(5)C_(1)(2x)^(4).Y^(1)+^(5)C_(2)(2x)^(3).Y^(2)`
`+^(5)C_(3)(2x)^(2).Y^(3)+^(5)C_(4)(2x)^(1).Y^(4)+^(5)C_(5).Y^(5)`
`=1.32x^(5)+5.16x^(4)y+10.8x^(3)y^(2)+10.4x^(2)y^(3)`
`+5.2xy^(4)+1.^(5)`
`=32x^(5)+80x^(4)Y+80x^(3)y^(2)+40x^(2)y^(3)+10xy^(4)+y^(5).`
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