Question

Factories 125a³+b³/27

Answer 1

(5a+b/3)(25a^2-5ab/3+b/9)

Answer 2

Answer:

To factorise 125a³ + b³/27

By looking at the question, we come to the conclusion that both the terms are perfect cubes. Hence we how to find a identity which can incorporate it.

we can find answer through the following identity

identity :

$\boxed{x^3 +y^3 = (x+y)(x^2 -xy+y^2)}$

substitute the values  in it

x³ = 125a³

y³= b³/27

⇒ x = 5a

⇒ y = b/3

x³+y³ =125a³+b³/27  thus , we get

⇒ 125a³+ b³/27 = (5a+b/3)(25a²-5ab/3 + b²/9)

$\\also,\boxed{x^3 -y^3 = (x-y)(x^2 +xy+y^2)}$