Question

सोपे रूप द्या: (x + y)³ - (x - y)³

Answer 1

सोपे रूप द्या: (x + y)³ - (x - y)³

${a}^{3} - {b}^{3} = (a - b)( {a}^{2} + ab + {b}^{2} ) \\ \\ a = (x + y) \\ \\ b = (x - y) \\ \\ {(x + y)}^{3} - {(x - y)}^{3} \\ \\ = [(x + y) -(x - y)][{(x + y)}^{2} +(x + y)(x - y) + {(x - y)}^{2} ] \\ \\ = (x + y - x + y)( {x}^{2} + {y}^{2} + 2xy + {x}^{2} - {y}^{2} + {x}^{2} + {y}^{2} - 2xy) \\ \\ {(x + y)}^{3} - {(x - y)}^{3}= (2y)(3 {x}^{2} + {y}^{2} )$