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Do you always use the property of distribution when multiplying monomials and polynomials?

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The short answer is YES.

The Distributive Property is an algebra property which is used to multiply a single term and two or more terms inside a set of parentheses. 

example: 2*(3+5) = 2*3 + 2*5 = 16.  we "distribute" the 2 'over' the additon of 3 and 5.

distribution becomes important when we look at the example:

2 * 3+5  which = 11 AND IS NOT THE SAME AS ABOVE