Factorise : (a²-b²)³ + (b²-c²)³ +(c² - a²)³
.I know it's quite tough.. Plz help me ..◾♥◾
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Factorise : (a²-b²)³ + (b²-c²)³ +(c² - a²)³
.I know it's quite tough.. Plz help me ..◾♥◾
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We are given to factorise ( a² - b² )³ + ( b² - c² )³ + ( c² - a² )³
It look very hard but if u recall algebraic identities it is very easy to factorise
The algebraic identity that we need here is :
Now coming back to the question
( a² - b² )³ + ( b² - c² )³ + ( c² - a² )³
So according to the identity let's check the value of x + y + z
Here
⇒ x + y + z = a² - b² + b² - c² + c² - a² = 0
Since it satisfies the if part it is obvious that it also satisfies then part of the algebraic identity
⇒ x³ + y³ + z³ = ( a² - b² )³ + ( b² - c² )³ + ( c² - a² )³
= 3( a² - b² )( b² - c² )( c² - a² ) [ ∵ If x + y + z = 0 ⇔ x³ + y³ + z³ = 3xyz ]
Hence factorised !