Question

Factorize each of the following expressions:
x³/216 -8y³

Answer 1

The algebraic expression is given as :  x³/216 - 8y³

= (x/6)³ + (2y)³

In order to factorise the given algebraic expression as the differences of two cubes we use the following identities - a³ - b³ = (a -  b) (a² + ab + b²) :  

Here a = x/6 and b = 2y

= (x/6 - 2y) ((x/6)² + x/6 × 2y + (2y²))

= (x/6 - 2y) (x²/36 + xy/3 + 4y²)

Hence,  the factorization of an algebraic expression is (x/6 - 2y) (x²/36 + xy/3 + 4y²).

 

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Answer 2

Step-by-step explanation:

a³ - b³ = (a -  b) (a² + ab + b²) :  

Here a = x/6 and b = 2y

= (x/6 - 2y) ((x/6)² + x/6 × 2y + (2y²))

= (x/6 - 2y) (x²/36 + xy/3 + 4y²)

Hence,

 the factorization of an algebraic expression is (x/6 - 2y) (x²/36 + xy/3 + 4y²).