Expand: `((x^(2))/(2)-(y^(2))/(3))^(6)`

Explanation

By Using binomial theorem, we have
`((x^(2))/(2)-(y^(2))/(6))^(6)=.^(6)C_(0)((x^(2))/(2)^(6)-.^(6)C_(1)((x^(2))/(2)^(5)((y^(2))/(3))+.^(6)C_(2)((x^(2))/(2))^(4)((y^(2))/(3))^(2)-.^(6)C_(3)((x^(2))/(2))^(3)((y^(2))/(3))^(3)` . . . .
`.^(6)C_(4)((x^(2))/(2))^(2)((y^(2))/(3))^(4)-.^(6)C_(5)((x^(2))/(2))((y^(2))/(3))^(5)+.^(6)C_(6)((y^(2))/(3))^(6)`
`=(x^(12))/(64)-6.(x^(10))/(32)*(y^(3))/(3)+15((x^(8))/(16))(y^(4))/(9))-20((x^(6))/(8))(y^(6))/(27))+15((x^(4))/(4))((y^(8))/(81))-6*((x^(2))/(2))((y^(10))/(243))+(y^(12))/(729)`
`=(x^(12))/(64)-(x^(10)y^(2))/(16)+(5x^(8)y^(4))/(48)-(5x^(6)y^(6))/(54)+(5x^(4)y^(8))/(108)-(x^(2)y^(10))/(81)+(y^(12))/(729)`.