Evaluating a function

Let the function f(a,b) be defined as f(a,b) = b² - a.
For all x and y, f((x² + y²),(x - y)) = ?
A.)  2y²
B.)  0
C.)  -2y²
D.)  -2xy + 2y²
​E.)  -2xy

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Substitute (x² + y²) in for a, and (x - y) in for b, into b² - a.

f(a,b) = b² - a
f((x² + y²), (x - y) = (x - y)² - (x² + y²)   {substituted (x² - y²) for a and (x - y) for b into b² - a}
=  (x - y)(x - y) - x² - y²   {squared the binomial and removed parentheses on second binomial, distributing negative sign}
=  x² - 2xy + y² - x² - y²   {used distributive property / FOIL method}
=  -2xy   {combined like terms}

E.)  -2xy

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