Using binomial theorem, expand each of the following:`(sqrt(x)+sqrt(y))^(8)`

Answer

`x^(4)+8x^(7//2)y^(1//2)+28x^(3)y+56x^(5//2)y^(3//2)+70x^(2)y^(2)+56x^(3//2)y^(5//2)+28xy^(3)+8x^(1//2)y^(7//2)+y^(4)`

Explanation

`(x^(1+2)+y^(1//2))^(8)`
`=.^(8)C_(0)(x^(1//2))^(8) + .^(8)C_(1)(x^(1//2))^(7)(y^(1//2))+.^(8)C_(2)(x^(1//2))^(6)(y^(1//2))^(2)+.^(8)C_(3)(x^(1//2))^(5)(y^(1//2))^(3)`
`+.^(8)C_(4) (x^(1//2))^(4)(y^(1//2))^(4)+.^(8)C_(5)(x^(1//2))^(3)(y^(1//2))^(5)+.^(8)C_(6)(x^(1//2))^(2)(y^(1//2))^(6)+.^(8)C_(7)(x^(1//2))(y^(1//2))^(7)+.^(8)C_(8)(y^(1//2))^(8)`
`x^(4)+8x^(7//2)y^(1//2)+28x^(3)y+56x^(5//2)y^(3//2)+70 x^(2) y^(2)+56x^(3//2)y^(5//2)+28xy^(3)+8x^(1//2)y^(7//2)+y^(4).`