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