Question

simplify by adding like terms:
`2xyx + 3yx {y}^(2) - 3 {x}^(2) y + 5 {y}^(3)x - 6y {x}^(2)`

Answer 1

To solve the exercise you can use this law of exponents:

`x^m\cdot x^n=x^(m+n)`

So, rewriting the polynomial with the help of the previous law, you have

`\begin{gathered} 2xyx+3yxy^2-3x^2y+5y^3x-6yx^2=2x^(1+1)y+3xy^(2+1)-3x^2y+5y^3x-6yx^2 \\ 2xyx+3yxy^2-3x^2y+5y^3x-6yx^2=2x^2y+3xy^3-3x^2y+5y^3x-6yx^2 \\ \text{ Rearranging the monomials according to the literal part} \\ 2xyx+3yxy^2-3x^2y+5y^3x-6yx^2=2x^2y+3xy^3-3x^2y+5xy^3-6x^2y \end{gathered}`

Finally, operate monomials that have the same literal part

`2xyx+3yxy^2-3x^2y+5y^3x-6yx^2=-7x^2y+8xy^3`

Therefore, the simplified polynomial is

`-7x^2y+8xy^3`