Questions: Let f(x, y) = x^2 - 2xy - y^2. Compute f(3,0) and f(3,-2). f(3,0) = (Simplify your answer.) f(3,-2) = (Simplify your answer.)

Transcript text: Let $f(x, y)=x^{2}-2 x y-y^{2}$. Compute $f(3,0)$ and $f(3,-2)$. $f(3,0)=$ $\square$ (Simplify your answer.) \[ f(3,-2)= \] $\square$ (Simplify your answer.)

Solution

Solution Steps

Step 1: Compute $ f(3, 0) $

Given the function $ f(x, y) = x^{2} - 2xy - y^{2} $, substitute $ x = 3 $ and $ y = 0 $: \[ f(3, 0) = (3)^{2} - 2(3)(0) - (0)^{2} = 9 - 0 - 0 = 9. \]

Step 2: Compute $ f(3, -2) $

Substitute $ x = 3 $ and $ y = -2 $ into the function: \[ f(3, -2) = (3)^{2} - 2(3)(-2) - (-2)^{2} = 9 + 12 - 4 = 17. \]