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;
![3( x + 3 ) = 3x + 9,\\3( x ) + 3( 3 ) = 3x + 9,\\\\3( x ) = 3x,\\3( 3 ) = 9,\\\\3x + 9 = 3x + 9](https://tex.z-dn.net/?f=3%28%20x%20%2B%203%20%29%20%3D%203x%20%2B%209%2C%5C%5C3%28%20x%20%29%20%2B%203%28%203%20%29%20%3D%203x%20%2B%209%2C%5C%5C%5C%5C3%28%20x%20%29%20%3D%203x%2C%5C%5C3%28%203%20%29%20%3D%209%2C%5C%5C%5C%5C3x%20%2B%209%20%3D%203x%20%2B%209)
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;
![2 + 3 + 4 = 4 + 3 + 2,\\2 - 2,\\3 - 3,\\4 - 4\\\\True!](https://tex.z-dn.net/?f=2%20%2B%203%20%2B%204%20%3D%204%20%2B%203%20%2B%202%2C%5C%5C2%20-%202%2C%5C%5C3%20-%203%2C%5C%5C4%20-%204%5C%5C%5C%5CTrue%21)
...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.