InterviewSolution
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InterviewSolution
| 1. |
Factorise (a²-b²)³-(b²-c²)³+(c²-a²)³ |
| Answer» (a²-b²)³+(b²-c²)³+(c²-a²)³=3(a+b)(b+c)(c+a)(a-b)(b-c)(c-a)We know that if x + y + z =0 then x3\xa0+ y3\xa0+ z3\xa0= 3xyzHere x = a²-b², y = b²-c² and z = c²-a²a²-b² + b²-c² + c²-a² = 0Hence (a²-b²)³+(b²-c²)³+(c²-a²)³ = 3(a²-b²)(b²-c²)(c²-a²)³= 3(a + b)(a − b)(b + c)(b − c)(c + a)(c − a)= 3(a + b)(b + c)(c + a)(a − b)(b − c)(c − a) | |