Question

find the highest common factor of x^4 -y^4 and x^2-2xy+y^2

Answer 1

Hi Friend !!!

Here is ur answer !!!

x^4 - y ^4 = (x²+y²)(x+y)(x-y)

x²-2xy+y² = (x-y) (x-y)


Highest common factor =>

x-y


Hope it helps u :-)

Answer 2

To Get the highest common factor, we have to get the factor first.


First, factorising x⁴ - y⁴ :


x⁴ - y⁴

→ ( x² )² - ( y² )²

→ ( x² + y² ) ( x² - y² )

→ ( x² + y² )( x - y )( x + y )



Then, factorising x² - 2xy + y²

→ x² - xy - xy + y²

→ x( x - y ) - y( x - y )

→ ( x - y )( x - y )




Hence,

x⁴ - y⁴ = ( x² + y² )( x - y )( x + y )


x² - 2xy + y² = ( x - y )( x - y )




Highest common factor is the factor which is highest in all the common factors. Here ( x - y ) is that factor which is common in both.




Therefore, Highest Common Factor of x⁴ - y⁴ and x² - 2xy + y² is ( x - y )

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