Question

Factorize it : a(b2-c2)+b(c2-a2)+c(a2-b2)

Answer 1

Given: The term a(b²-c²)+b(c²-a²)+c(a²-b²)

To find: Simplify the above term.

Solution:

   Now we have given the term a(b²-c²)+b(c²-a²)+c(a²-b²)

   Multiplying it, we get:

                  ab²- ac² + bc² - a²b + c ( a² - b² )

                  ab² - a²b - ac² + bc² + c ( a - b )( a + b )

                  -ab( a - b ) - c²( a - b ) + c ( a - b )( a + b )

   Taking a - b common, we get:

                  ( a - b ) x ( -ab - c² + ac + bc )

                  ( a - b ) x ( -ab + ac - c² + bc )

                  ( a - b ) x ( -a( b - c ) + c ( b - c ) )

                  ( a - b ) x ( c - a ) x ( b - c )

Answer:

          So the simplified form is ( a - b ) x ( c - a ) x ( b - c ) .