Question

Factorise the following expressions X^7y^7-xy

Answer 1

Given: The term (x^7y^7 - xy)

To find: Factorise the given expression.

Solution:

• Now we have given the expression x^7y^7 - xy.

• Taking xy common, we get:

              xy ( x^6y^6 - 1 )

              xy ( (xy)^6 - 1 )

              xy ( ((xy)^2)^3 - 1^3 )

• Now we have the formula for a^3 - b^3 - (a-b)(a^2 + ab + b^2).

• So applying it, we get:

              xy ((xy)^2 - 1 ) (((xy)^2)^2 + (xy)^2 + 1 )

              xy (xy - 1)(xy + 1)(((x^4y^4 + x^2y^2 + 1 )

Answer:

        So the factors of given terms are

         xy (xy - 1)(xy + 1)(((x^4y^4 + x^2y^2 + 1 )