Question

Simplify (a 2 -b 2 ) 3 +(b 2 -c 2 ) 3 +(c 2 -a 2 ) 3 divided by (a-b) 3 +(b-c) 3 +(c-a) 3

Answer 1

Hi ,

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We know that ,

If x + y + z = 0

then

x³ + y³ + z³ = 3xyz

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Now ,

i ) Let x = a² - b² ,

y = b² - c²

z = c² - a²

x + y + z = a² - b² + b² - c² + c² - a²

= 0

Therefore ,

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

= 3( a² - b² )( b² - c² )( c² - a² ) ---( 1 )

Similarly ,

ii ) ( a - b )³ + ( b - c )³ + ( c - a )³

= 3( a - b )( b - c )( c - a ) ----( 2 )

Now ,

( 1 ) ÷ ( 2 )

=[3(a²-b²)(b²-c²)(c²-a²)]/[3(a-b)(b-c)(c-a)]

= ( a + b )( b + c )( c + a )

I hope this helps you.

: )

Answer 2

Answer:

Hope This Helps You...................................