Rebecca R. answered • 02/20/14

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Polynomials are made up of monomials, so if you want to simplify anything down, you will always have to use the distributive property. The only cases when you don't have to use the distributive property are when you are multiplying pure monomials.

For example:

When multiplying (3x

^{2}+ 2x - 1) * (x + 2 ) if you don't use distribution, you have no way to simplify the expression at all.On the other hand, if you were just doing (3x)(2)(5x), you can multiply them together without using the distributive property because they are all monomial expressions.