Question

Factorise : (a²-b²)³ + (b²-c²)³ +(c² - a²)³


.I know it's quite tough.. Plz help me ..◾♥◾​

Answer 1

Step-by-step explanation:

hlo mate .

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Hope it helps u little...

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Answer 2

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 :

• If x + y + z = 0   ⇔    x³ + y³ + z³ = 3xyz

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 = a² - b²
• y = b² - c²
• z = c² - a²

⇒ 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 !