Sure! Let's analyze and simplify the given expression step-by-step.
Given expression: [tex]\(-20\pi k - 2r^2\)[/tex]
1. Identify the coefficients and variables:
- The term [tex]\(-20\pi k\)[/tex] has a coefficient of [tex]\(-20\pi\)[/tex] and a variable [tex]\(k\)[/tex].
- The term [tex]\(-2r^2\)[/tex] has a coefficient of [tex]\(-2\)[/tex] and a variable [tex]\(r^2\)[/tex].
2. Describe each part individually:
- [tex]\(-20\pi k\)[/tex]: This term includes [tex]\(\pi\)[/tex], a mathematical constant approximately equal to 3.14159, multiplied by -20 and then by the variable [tex]\(k\)[/tex].
- [tex]\(-2r^2\)[/tex]: Here, [tex]\(r^2\)[/tex] represents the variable [tex]\(r\)[/tex] squared (multiplied by itself), and it is then multiplied by -2.
3. Combine both parts:
Since there are no like terms (terms having the same variable raised to the same power), they cannot be directly combined. The expression remains as a sum of both parts:
[tex]\[
-20\pi k - 2r^2
\][/tex]
There is nothing further to simplify in this expression, because:
- [tex]\(k\)[/tex] and [tex]\(r\)[/tex] are different variables and not like terms.
- The coefficients are not additive or multipliable directly with each other.
So, the simplified final form of the expression is [tex]\(-20\pi k - 2r^2\)[/tex].
