The commutative property of multiplication states that changing the order of the factors does not change the product. In other words, \( a \times b = b \times a \).
Now, let's analyze your options:
a. \( 3 (b^{10} + 4) = 3 (4 + b^{10}) \)
This shows the commutative property of addition inside the parentheses, but it doesn't directly demonstrate the commutative property of multiplication.
b. \( z^{11} \cdot (2 z^{11} + 2) \)
This expression does not demonstrate the commutative property of multiplication.
c. \( 11(b + z) = 11b + 11z \)
This demonstrates the distributive property, not the commutative property.
d. \( 2 (b^{10} + z^{11}) = (b^{10} + z^{11}) \cdot 2 \)
This demonstrates the commutative property of multiplication, as it shows that multiplying by 2 can occur before or after the sum.
Among the given choices, d correctly demonstrates the use of the commutative property of multiplication.