Question

factorise the following: 81x³-3y³​

Answer 1

Answer:

Here's your answer;

We are given an equation to factorise, which is as follows:

81x³ - 3y³

Now, we know that the following equation can also be written as,

81x³ - 3y³ = 3( 27x³ - y³ )

Now, solving RHS,

= 3 [ (3x)³ - (y)³ ]

Using the Identity, a³ - b³ = ( a - b ) ( a² + ab + b² )

⇒ 3 [ (3x - y) ( (3x)² + 3xy + y²) ]

Or,

81x³ - 3y³ = 3 [ (3x - y) ( 9x² + 3xy + y² ) ]

Hope, this helps.