The Commutative Property of Multiplication states that changing the order of the factors does not change the product. In other words, \( a \times b = b \times a \).
Looking at the options provided:
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\( 2(b^{10} + z^{11}) = (b^{10} + z^{11}) \times 2 \): This shows associative behavior rather than commutative property, but it does maintain the form of a multiplication since both sides are equivalent.
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\( z^{11} \times 2 = z^{11} + 2 \): This is not correct. It incorrectly states that multiplication is equal to addition.
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\( 3(b^{10} + 4) = 3(4 + b^{10})3 \): This seems to be incorrectly written because of the extra '3' at the end. Even without that, this does not directly demonstrate the commutative property.
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\( 11(b + z) = 11b + 11z \): This demonstrates the Distributive Property, not the Commutative Property.
None of the options explicitly demonstrates the Commutative Property of Multiplication. However, if we were to correct the third example by removing the extra '3', it would more accurately reflect the property intended: \( 3(b^{10} + 4) = 3(4 + b^{10}) \) would show the order of addition is being altered, but we would primarily need it to reflect multiplication.
In conclusion, none of these options correctly demonstrate the Commutative Property of Multiplication as stated. If you were looking for an example of the commutative property, it would look like \( a \times b = b \times a \).
2 answers