Question

Can anyone assist me with these?

Answer 1

Option A. Distributive Property,

Option B. Commutative Property,

Option C. Associative Property,

Option D. Associative Property

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`

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!`

...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.