Question

which of the following correctly demonstrates the use of the commutative property of multiplication
a. 3 (b^10 + 4) = 3 (4+b^10) 3
b. z^11 dot 2 z^11 + 2
c. 11(b+z) = 11b + 11z
d. 2 (b^10+ z^11) = (b^10+z^11) dot 2

Answer 1

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.