Question

(a^2-b^2)^3+(b^2-c^2)^3+(c^2-a^2)^3/(a-b)^3+(b-c)^3+(c-a)^3=(a+b)(b+c)(c+a)

Answer 1

Answer:

If x + y + z = 0 then x³ + y³ + z³ = 3xyz*******************************************Now ,i ) Let x = a² - b² ,y = b² - c² z = c² - a²x + y + z = a² - b² + b² - c² + c² - a²= 0Therefore ,( 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 )

Step-by-step explanation: