Question

factorize 1) (5a-3b)^3 -(5a+3b)^3 2) (5x+7y)^3-(5x-7y)^3

Answer 1

$1) \: {(5a - 3b)}^{3} - {(5a + 3b)}^{3} \\ we \: have \: {x}^{3} - {y}^{3} = (x - y)( {x}^{2} + {y}^{2} + xy)\\ = (5a - 3b - 5a - 3b)(25 {a}^{2} + 9 {b}^{2} - 30ab + 25 {a}^{2} + 9 {b}^{2} + 30ab + 25 {a}^{2} - 9 {b}^{2} ) \\ = ( - 6b)(75 {a}^{2} + 9 {b}^{2} ) \\ = - 18b(25 {a}^{2} + 3 {b}^{2} )\\ 2) \: {(5x + 7y)}^{3} - {(5x - 7y)}^{3} \\ = (5x + 7y - 5x + 7y)(25 {x}^{2} + 49{y}^{2} + 70xy + 25 {x}^{2} + 49 {y}^{2} - 70xy + 25 {x}^{2} - 49 {y}^{2} ) \\(14y)(75 {x}^{2} + 49 {y}^{2} )$