Answer
(a) Yes. $4xy^3-5x^3y$ is in simplified form
(b)No. Simplified form is $-y+1$.
(c) No. Simplified form is $5x^2+9xy$.
Work Step by Step
Distributive law is expressed as $a \cdot (b+c)=ab+ac$.
(a). In $4xy^3-5x^3y$, there exists no like terms which can be combined. Except using distributive law makes taking common factors out which actually doesn't imply simplified form. Distributive law can be used in reverse as $xy(4y^2-5x^2)$ which is not simplified form. Therefore. Given expression is already in simplified form.
(b) The expression $-(y-1)$ can be simplified using distributive law as $(-1)\cdot y+ (-1)\cdot (-1)=-y+1$.
(c) in the expression $5x^2+12xy-3yx$, the terms $12xy$ and $-3yx$ are like terms. So, their coefficients can be combined to simplify as $5x^2+9xy$.
