Question

Factorize: 27a^3 -(3a-b)^3

Answer 1

hope you answer helps u .....I am not sure about the factorization but I am really confident about the method ...

Answer 2

The answer is given below :

Now,

$27 {a}^{3} - {(3a - b)}^{3} \\ \\ = {(3a)}^{3} - {(3a - b)}^{3} \\ \\ = (3a - 3a + b)( {(3a)}^{2} + 3a(3a - b) + {(3a - b)}^{2} ) \\ \\ = b(9 {a}^{2} + 9 {a}^{2} - 3ab + 9 {a}^{2} - 6ab + {b}^{2} ) \\ \\ = b(27 {a}^{2} - 9ab + {b}^{2} )$

which is the required factorization.

Thank you for your question.