Can I change the order of two terms when factoring: $x^2(x^2-4-3x)$ to $x^2(x^2-3x-4)$?

Question

I'm doing homework and I'm stuck on this assignment: $$x^4 - 4x^2 - 3x^3$$

I figured this would equal $$x^2(x^2-4-3x)$$

Now I know if I would change the order to $$x^2(x^2-3x-4)$$

I can factorise it again, but my question is if it's allowed changing the order like that in algebra.

Answer 1

Yes, the law of commutativity (together with the law of associativity) allows you to rearrange summands (or factors) in arbitrary order. (However, because these laws hold for addition, not for subtraction, You better view the minus sign as part of the coefficient for this, i.e. $x^2-4-3x=x^2+(-4)+(-3x) = x^2+(-3x)+(-4) = x^2-3x-4$, just to prevent you from falling for $x-5=5-x$ or the like)

Answer 2

Yes you can do so as addition of real numbers is commutative.(Considering $x\in R$)

Addition is commutative means $\forall x,y\in R$ , $(x+y)=(y+x)$