Let's simplify the expression [tex]\(4r^2 - 8y^4\)[/tex] step-by-step.
1. Factor out the common factor:
Look at both terms in the expression to identify any common factors. Here, we see that both terms have a common factor of 4.
[tex]\[
4r^2 - 8y^4 = 4(r^2 - 2y^4)
\][/tex]
2. Examine the remaining expression inside the parentheses:
After factoring out the 4, we have [tex]\(r^2 - 2y^4\)[/tex] left inside the parentheses. Check if we can simplify or factor this expression further.
- [tex]\(r^2 - 2y^4\)[/tex]: There are no further factors or simplifications that can be done with the remaining expression in a way that would result in a simpler form.
So, the simplified expression can be written as:
[tex]\[
4(r^2 - 2y^4)
\][/tex]
However, since extracting a common factor is also a way of simplifying, and further simplification isn't possible beyond this, we recognize that the factorized form and the original expression are equivalently simplified.
Thus, we end up with the same form of the initial expression:
[tex]\[
4r^2 - 8y^4
\][/tex]
