Question

सोपे रूप द्या: (3xy - 2ab)³ - (3xy + 2ab)³

Answer 1

सोपे रूप द्या: (3xy - 2ab)³ - (3xy + 2ab)³

${(3xy - 2ab)}^{3} - {(3xy + 2ab)}^{3} \\ \\ {w}^{3} - {z}^{3} = (w - z)( {w}^{2} + wz + {z}^{2} ) \\ \\ here \\ \\ w = 3xy - 2ab \\ \\ z = 3xy + 2ab \\ \\ {(3xy - 2ab)}^{3} - {(3xy + 2ab)}^{3} \\ \\ = (3xy -2ab - 3xy - 2ab) \\ \\ ( {(3xy - 2ab)}^{2} + (3xy + 2ab)(3xy - 2ab)+ {(3xy + 2ab)}^{2} ) \\ \\ = ( - 4ab)(9 {x}^{2} {y}^{2} + 4 {a}^{2} {b}^{2} - 12xyab + 9 {x}^{2} {y}^{2} - 4 {a}^{2} {b}^{2} + 9 {x}^{2} {y}^{2} + 4 {a}^{2} {b}^{2} + 12xyab) \\ \\ = ( - 4ab)(27 {x}^{2} {y}^{2} + 4 {a}^{2} {b}^{2} )$
${(3xy - 2ab)}^{3} - {(3xy + 2ab)}^{3} = ( - 4ab)(27 {x}^{2} {y}^{2} + 4 {a}^{2} {b}^{2} )$