For all x and y, f((x² + y²),(x - y)) = ?

A.) 2y²

B.) 0

C.) -2y²

D.) -2xy + 2y²

E.) -2xy

**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**

**- Algebra House**