Simplification of Algebraic Expressions

Mathematical Expressions Simplification

Given Expression

The primary expression to simplify is:
$16x^{2}y^{2} ext{ (added or subtracted based on context)} \pm 2y^{1}z^{3}$

Steps for Simplification

1. Identifying Terms:

   • The first term is $16x^{2}y^{2}$.
   • The second term is $2y^{1}z^{3}$.

2. Common Factors:

   • Look for any common factors between the terms.
   • In this case, there is a common factor of $2y^{1}$ (the lowest power of y).

3. Factoring Out Common Factors:

   • Factoring out the common term gives:
     $2y^{1}(8xy^{1} ext{ (this represents from the first term)} ext{ (plus or minus) } z^{3})$

4. Final Expression:

   • The simplified expression can be represented as:
     $2y^{1}(8xy^{1} ext{ (plus or minus) } z^{3})$

Conclusion

The expression, after factoring out the common term, simplifies to:
$2y^{1}(8xy^{1} ext{ (plus or minus) } z^{3})$