Question

Factorise each of the given : 27-125a³-135a+225a²

Answer 1

Hello!

$\star\: \bf\small{IDENTITY\: USED}$ :
$\sf (a-b)^{3} = a^{3}-3a^{2}b+3ab^{2}-b^{3}$

$\star\: \bf\small{ANSWER}$ :

$\sf 27 - 125a^{3}- 135a + 225a^{2} \\ \\ \implies \sf (3)^{3}-(5a)^{3}- 3\times(3)^{2}\times5a + 3\times3\times(5a)^{2} \\ \\ \implies \boxed{\red{\bf{(3-5a)^{3}}}}$

Cheers!

Answer 2

Answer:

$(3\ -\ 5a)(3\ -\ 5a)(3\ -\ 5a)$

Step-by-step explanation:

According to the question

The given expression is :

$27\ -\ 125a^{3}\ -\ 135a\ +\ 225a^{2}$

Now, we have to factorize the above expression

$27\ -\ 125a^{3}\ -\ 135a\ +\ 225a^{2}$

It can be written as

$= (3)^{3}\ -\ (5a)^{3}\ -\ 3(3)^{2}(5a)\ +\ 3(3)(5a)^{2}$

= $(3\ -\ 5a)^{3}$ (Using the formula $(a\ -\ b)^{3} = a^{3}\ -\ b^{3}\ -\ 3a^{2}b\ +\ 3ab^{2})$

= $(3\ -\ 5a)(3\ -\ 5a)(3\ -\ 5a)$  (Answer)