To find the sum of the two expressions [tex]\(\left(x^2-x^4\right) + \left(x^4 - x^2\right)\)[/tex], we will add them term by term, combining like terms.
1. Write down both expressions clearly:
[tex]\[
\left(x^2 - x^4\right)
\][/tex]
[tex]\[
\left(x^4 - x^2\right)
\][/tex]
2. Add the expressions vertically by aligning like terms:
[tex]\[
\begin{array}{r}
x^2 - x^4 \\
+(x^4 - x^2)
\end{array}
\][/tex]
3. Combine the like terms:
- Combine the [tex]\(x^4\)[/tex] terms: [tex]\(-x^4 + x^4 = 0\)[/tex]
- Combine the [tex]\(x^2\)[/tex] terms: [tex]\(x^2 - x^2 = 0\)[/tex]
4. Write out the result:
[tex]\[
0
\][/tex]
Hence, the sum of the expressions [tex]\(\left(x^2-x^4\right) + \left(x^4-x^2\right)\)[/tex] simplifies to [tex]\(0\)[/tex].
