`(x+(y)/(2))^(3)+(2x-(y)/(2))^(3)` को सरल कीजिए ।

Explanation

यहाँ `(x+(y)/(2))^(3)=x^(3)+((y)/(2))^(3)+3(x)((y)/(2))(x+(y)/(2))`
`=x^(3) + (y^(3))/(8)+(3)/(2)xy(x+(y)/(2))" "...(1)`
पुन: `(2x-(y)/(2))^(3)=(2x)^(3)-((y)/(2))^(3)-3(2x)((y)/(2))(2x-(y)/(2))`
`=8x^(3)-(y^(3))/(8)-3xy(2x-(y)/(2))" "...(2)`
समीकरण (1) व (2) से
`(x+(y)/(2))^(3)+(2x-(y)/(2))^(3)=x^(3)+(y^(3))/(8)+(3)/(2)xy(x+(y)/(2))+8x^(3)-(y^(3))/(8)-3xy(2x-(y)/(2))`
`= (x^(3)+8x^(3))+((y^(3))/(8)-(y^(3))/(8))+(3)/(2)x^(2)y+(3)/(4)xy^(2)-6x^(2)y + (3)/(2)xy^(2)`
`=9x^(3) - (9)/(2)x^(2)y+(9)/(4)xy^(2)`