The problem asks to identify which option demonstrates the distributive property.

The distributive property states that for any numbers $a$, $b$, and $c$: $a(b + c) = ab + ac$

Now, let's evaluate the choices:

• a.) $11 + (-11) = 0$: This shows the property of additive inverses, not distributive property.
• b.) $(2 \times 7) \times 9 = 2 \times (7 \times 9)$: This is the associative property of multiplication, not distributive.
• c.) $4 \times 3 = 3 \times 4$: This is the commutative property of multiplication, not distributive.
• d.) $6(5 + 2) = 6(5) + 6(2)$: This is a perfect example of the distributive property, as it follows the pattern $a(b + c) = ab + ac$.

Therefore, the correct answer is d.) $6(5 + 2) = 6(5) + 6(2)$.

Would you like more details on any of these properties? Here are 5 related questions:

1. What is the commutative property of multiplication?
2. How does the associative property differ from the distributive property?
3. Can the distributive property be used with subtraction?
4. Why does $11 + (-11) = 0$ demonstrate the additive inverse property?
5. How is the distributive property applied in algebra?

Tip: The distributive property helps simplify expressions, especially when variables are involved, making it a useful tool in algebra.