Rearrange and add the following.                                                  -y^ - z^ - xy +1+3xy+2y -3x^ -5+xy+3xy -z^

Let's rearrange and combine the like terms in the expression:

\[
-y^ - z^ - xy +1+3xy+2y -3x^ -5+xy+3xy -z^
\]

1. Group like terms together:

\[
\begin{aligned}
&(-y + 2y) &\text{(terms with } y) \\
&(-z^ - z^) &\text{(terms with } z^2) \\
&(-xy + 3xy + xy + 3xy) &\text{(terms with } xy) \\
&(-3x^) &\text{(term with } x^2) \\
&(+1 - 5) &\text{(constant terms)}
\end{aligned}
\]

2. Combine the terms:

\[
y: -y + 2y = y
\]

\[
z^2: -z^2 - z^2 = -2z^2
\]

\[
xy: -xy + 3xy + xy + 3xy = 6xy
\]

\[
x^2: -3x^2
\]

\[
\text{Constants: } +1 - 5 = -4
\]

3. Combine all the simplified terms:

\[
y - 2z^2 + 6xy - 3x^2 - 4
\]

So, the simplified expression is:

\[
y - 2z^2 + 6xy - 3x^2 - 4
\]

Would you like details on any step? Here are some related questions:

1. How do you combine like terms in algebraic expressions?
2. What are like terms and how do you identify them?
3. How does the order of operations affect combining terms?
4. Can you rearrange terms in any expression without affecting its value?
5. What is the significance of the coefficients in algebraic expressions?

**Tip:** Always check your work by ensuring all like terms are combined correctly and no terms are left out!

Learn how to rearrange and simplify the algebraic expression y - 2z^2 + 6xy - 3x^2 - 4 step-by-step. This problem covers combining like terms and simplifying expressions, essential concepts in algebra. Suitable for students in Grades 7-9.

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