Question

सोपे रूप द्या: (3a + 5b)³ - (3a - 5b)³

Answer 1

सोपे रूप द्या: (3a + 5b)³ - (3a - 5b)³

${x}^{3} - {y}^{3} = (x - y)( {x}^{2} + xy + {y}^{2} ) \\ \\ x = 3a + 5b \\ \\ y = 3a - 5b \\ \\ {(3a + 5b)}^{3} - {(3a - 5b)}^{3} \\ \\ = [(3a + 5b) - (3a - 5b)]( {(3a + 5b)}^{2} + (3a + 5b) (3a - 5b) + {(3a - 5b})^{2} ) \\ \\ = (3a + 5b - 3a + 5b)(9 {a}^{2} + 25 {b}^{2} + 30ab + 9 {a}^{2} - 25 {b}^{2} + 9 {a}^{2} + 25 {b}^{2} - 30ab) \\ \\ = 10b(27 {a}^{2} + 25 {b}^{2} )$

${(3a + 5b)}^{3} - {(3a - 5b)}^{3} =10b(27 {a}^{2} + 25 {b}^{2} )$