Question

27m cube 3 - 216n cube 3. Factorise. solve using this formula.
$a {}^{3 } - b {}^{3} = (a - b)(a {}^{2} + ab + b {}^{2} )$

Answer 1

Hey dear here is your answer........

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Answer 2

Hi friend, Harish here.

Here is your answer.

Given an identity , and let us transform the expression to solve  it using the given identity.

We know that :

27 = 3 × 3 × 3 = 3³      &     216 = 6 × 6 × 6 = 6³

Then,

27 m³  - 216 n³  =   (3m)³  -  (6n)³

Now lets proceed to the next step. So now we can directly apply the identity as they both are similar.

⇒  (3m)³  -  (6n)³ =  ( 3m - 6n ) ( 9m² + 18mn + 36n²)

Now we can also take 3 and 9 as common from the separate factors.

⇒ ( 3m - 6n ) ( 9m² + 18mn + 36n²)  = 27 ( m -2n ) ( m² + 2mn + 4n² )

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Hope  my answer is helpful to you.