Question

(3a+5b)3-(3a-5b)3 factories

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Answer 1

$(27 {a}^{2} + 25 {b}^{2} )10b$

Step-by-step explanation:

$Given, \: \: \: (3a + 5b)^{3} - (3a - 5b)^{3} \\ we \: \: know \: \: \boxed{ {x}^{3} - {y}^{3} = (x - y)( {x}^{2} + xy + {y}^{2} ) } \\ Now, \: \: \: (3a + 5b)^{3} - (3a - 5b)^{3} \\ = \{ (3a + 5b) - (3a - 5b)\} \{ (3a + 5b)^{2} + (3a + 5b)(3a - 5b) + (3a - 5b)^{2} \} \\ = \{ 3a + 5b - 3a + 5b\} \{(9 {a}^{2} + 30ab + 25 {b}^{2} ) + (9 {a}^{2} - 25 {b}^{2} ) + (9 {a}^{2} - 30ab + 25 {b}^{2} ) \} \\ = \{ 3a + 5b - 3a + 5b\} \{9 {a}^{2} + 30ab + 25 {b}^{2} + 9 {a}^{2} - 25 {b}^{2} + 9 {a}^{2} - 30ab + 25 {b}^{2} \} \\ = (10b)(27 {a}^{2} + 25 {b}^{2} ) \\ = \boxed{(27 {a}^{2} + 25 {b}^{2} )10b}$