Question

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Factorise:
x^7y^7 - xy​

Answer 1

Answer:

to factorize x⁷y⁷ - xy

=> xy [ x⁶y⁶ - 1 ]

=> xy [ (x²y²)³ - 1³ ] [ x³ - y³ = (x-y)(x² + xy + y²) ]

=> xy [ (x²y² - 1)(x⁴y⁴ + x²y² + 1²)

=> xy [ {(xy)² - 1²} { x⁴y⁴ + x²y² + 1} ] [x²-y²=(x+y)(x-y)]

=> xy [ (xy + 1)(xy - 1) (x⁴y⁴ + x²y² + 1 ) ]

=> xy (xy + 1)(xy - 1)(x⁴y⁴ + x²y² + 1)

Answer 2

Answer:

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 )

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