Certainly! Let's simplify the polynomial [tex]\( 100y^4 - 36y^2 + 1 \)[/tex].
1. Identify the Polynomial:
We start with the polynomial:
[tex]\[
100y^4 - 36y^2 + 1
\][/tex]
2. Group Terms:
Notice that this polynomial is already in its simplest grouped form. Each term is a single monomial.
3. Apply Polynomial Simplification Techniques:
In some cases, this might involve factoring, combining like terms, or using algebraic identities to condense the polynomial. However, we observe here that:
- The polynomial contains three terms.
- Each term is distinct and does not lend itself directly to further factoring or simplification using common algebraic identities (like difference of squares, cubes, etc.).
4. Verify Non-Simplifiability:
Check if [tex]\( 100y^4 - 36y^2 + 1 \)[/tex] can be factored:
- Look for common factors: The coefficients [tex]\( 100 \)[/tex], [tex]\( 36 \)[/tex], and [tex]\( 1 \)[/tex] do not have common factors, other than [tex]\( 1 \)[/tex].
5. Conclude the Simplification:
The polynomial [tex]\( 100y^4 - 36y^2 + 1 \)[/tex] does not simplify further:
[tex]\[
100y^4 - 36y^2 + 1
\][/tex]
remains as such after simplification.
Therefore, the simplified form of the polynomial [tex]\( 100y^4 - 36y^2 + 1 \)[/tex] is indeed still:
[tex]\[
100y^4 - 36y^2 + 1
\][/tex]
Thus, the polynomial is already in its simplest form.
