Answer:
Option A. Distributive Property,
Option B. Commutative Property,
Option C. Associative Property,
Option D. Associative Property
Step-by-step explanation:
Consider the first example, 3( x + 3 ) = 3x + 9. We can note that in order to derive " 3x + 9 " you had to distribute the 3 to x and 3 in ( ), as demonstrated below;
[tex]3( x + 3 ) = 3x + 9,\\3( x ) + 3( 3 ) = 3x + 9,\\\\3( x ) = 3x,\\3( 3 ) = 9,\\\\3x + 9 = 3x + 9[/tex]
And hence, this would be a perfect example of the distributive property.
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Now this second example, 2 + 3 + 4 = 4 + 3 + 2 is simply the re - arrangement of numbers;
[tex]2 + 3 + 4 = 4 + 3 + 2,\\2 - 2,\\3 - 3,\\4 - 4\\\\True![/tex]
...And is thus the perfect example of the commutative property.
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This third example we have an application of the associative property. The numbers are again being re - arranged and grouped, but with a multiplication sign between them.
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Last but not least the associative property. We have the grouping of numbers with a plus sign between, which indicates the associative property of addition.
