1. ## Polynomial Question

Since multiplication is basically addition, why can't unlike terms in polynomials be added or subtracted, but they can be multiplied?

2. Originally Posted by paulmo

I quite quite understand the question, do you have an example to consider?

3. For example, x^2y + 3xy cannot be simplified, but x^2y*3xy= 3x^2y^2, right? Just learning here.

4. Originally Posted by paulmo
For example, x^2y + 3xy cannot be simplified, but x^2y*3xy= 3x^2y^2, right? Just learning here.
Be careful $\displaystyle x^2y\times 3xy= 3x^3y^2$

But yes the first expression cannot be simplified.

5. OK, considering multiplication is addition, could you please explain why the first example can't be added, but unlike terms can be multiplied?

6. Originally Posted by pickslides
Be careful $\displaystyle x^2y\times 3xy= 3x^3y^2$
But yes the first expression cannot be simplified.
Hmmm.....xy(x + 3) ; no?

7. pickslides is referring to this one that can't be simplified:
$\displaystyle x^2y + 3xy$
I'm just curious why unlike terms can be multiplied, but not added, when multiplication is basically division.

8. Originally Posted by paulmo
pickslides is referring to this one that can't be simplified:
$\displaystyle x^2y + 3xy$
YES...so am I; I'm saying it CAN be simplified, to:
xy(x + 3)
WHY are you saying it can't be simplified?

9. My Barron's College Review Algebra book says that example--added unlike terms polynomial--cannot be simplified. Seems you've shown that's not true? But pickslides also says cannot be simplified. So what's the deal?

10. Originally Posted by paulmo
So what's the deal?
It's a mystery....

11. No offense, but I'm here to get answers from people who know more than I do, not to get smug responses.

12. Well, x^2y + 3xy can be simplified to xy(x + 3) : that's a fact.
So it's a MYSTERY that you're told otherwise.
If you don't like the word "mystery", change it to whatever you like.

13. Oh, OK. I get your simplification. I'm just wondering why a Barron's College Algebra would not have shown that as a simplification. I'm guessing books will not always be so comprehensive.

14. Well, your basic problem is thinking that "multiplication is basically addition" and that "multiplication is addition". That is simply not true. We can think of multiplication as "repeated addition", as pickslides said, but since the number of times we repeat the addition is itself a variable, addition and multiplication cannot be expected to have the same properties.

15. Thanks Halls, that is very helpful. So if multiplication, as addition, is communicative, how to tell what's the variable in $\displaystyle 3*5*8$ etc?

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