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Simplify the following:?


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1 Answer

  • 8 months ago

    Use the "difference of squares" factoring to write (y² - x²) as (y + x) (y - x).  Then the numerator becomes:

    (y + x) (y - x) (x - y)² = (x + y) (y - x) (x - y)²

    Now, so long as (x + y) is not zero, the (x + y) factors on top and bottom cancel out and you're left with just

    (y - x) (x - y)²

    But x - y = -(y - x), so (x - y)² = (y - x)² and you can rewrite that as:

    (y - x) (y - x)² = (y - x)³

    That's the simplest form I can see.

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