Question

factorise using suitable identity x⁶-y⁶​

Answer 1

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Answer 2

On factoring (x⁶-y⁶​) we will get (x+y)(x-y)(x⁴+y⁴+x²y²)  

Given:

x⁶-y⁶​

To find:

Factorise using suitable identity

Solution:

Given  x⁶-y⁶​

As we know a⁶ = (a²)³

⇒ x⁶-y⁶ = (x²)³ - (y²)³  

From algebraic identity  a³- b³ = (a-b)(a²+b²+ab)

= (x²)³ - (y²)³  

= (x² - y²) [ (x²)²+ (y²)² + x²y² ]  

= (x² - y²) [ x⁴+ y⁴ + x²y² ]    

From algebraic identity a²- b² = (a-b)(a+b)

⇒ (x²- y²) = (x+y)(x-y)

= (x+y)(x-y)(x⁴+ y⁴ + x²y²)  

Therefore,

On factoring (x⁶-y⁶​) we will get (x+y)(x-y)(x⁴+y⁴+x²y²)  

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