Final answer:
The expression that equals zero when x = 3 and y = -3 is x² - y².
Therefore, the correct answer is: option (1) x² - y².
Step-by-step explanation:
To find the correct expression, we substitute the values of x and y into each expression and simplify.
x² - y² = (3)² - (-3)²
= 9 - 9
= 0.
So, expression (1) equals zero.
x² + y² = (3)² + (-3)²
= 9 + 9
= 18.
This expression does not equal zero.
xy = 3 * (-3) = -9.
This expression does not equal zero.
x - y = 3 - (-3)
= 3 + 3
= 6.
This expression does not equal zero.
Therefore, the expression that equals zero when x = 3 and y = -3 is (1) x² - y².