Can someone tell me if I'm correct? The property of polynomial multiplication that allows us to combine like terms like this: 2x^3 + 5x^3 = 7x^3 is ASSOSCIATIVE.

Question

tkhunny · Answer

Hmmm....  No.  You have changed no association.

2x^3 + 5x^3 = (2+5)x^3

Look familiar, yet?

anonymous · Answer

Commutative?

tkhunny · Answer

This is commutative: a*b*c = a*c*b -- See how we changed the order of things?
This is associative: (a*b)*c = a*(b*c) -- See how we just grouped them differently?
See also how there is ONLY multiplication going on, here?

This is commutative: a + b + c = a + c + b -- See how we changed the order of things?
This is associative: (a+b)+c = a+(b+c) -- See how we just grouped them differently?
See also how there is ONLY addition going on, here?

You have a property that involves both multiplication AND addition.

anonymous · Answer

I get it. So then it has to be distributive?

tkhunny · Answer

Yes!  The Distributive Property of Multiplication over Addition.  Sometimes it helps to use the whole name, albeit quite tedious.

anonymous · Answer

Alright. I understand it now. Thank you very much