To determine which of the following demonstrates the use of the commutative properties of multiplication, let's first clarify what the commutative property states.
Commutative Property of Multiplication: This property 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 both expressions:
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11(b + z) = 11b + 11z: This expression demonstrates the distributive property, not the commutative property. The distributive property states that \( a(b + c) = ab + ac \).
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3(b^10 + 4) = 3(4 + b^10)3: Although this expression appears to attempt to use the commutative property by rearranging the terms inside the parentheses, it also improperly represents the equality with the extra factor of "3" at the end.
Correctly recognizing and applying the commutative property would involve simply rearranging the operands of multiplication or addition without changing how they are used in expressions, such as \( b \times 4 = 4 \times b \).
Since neither option correctly illustrates the use of the commutative property of multiplication, neither expression is valid in demonstrating that property.
If you are looking for an expression that correctly demonstrates the commutative property of multiplication, it could look like this:
- \( 3b = b3 \) or
- \( 2 \times 5 = 5 \times 2 \).
Both showcase the interchangeability of factors in multiplication.
1 answer