To solve the expression [tex]\(-r^2 \left( r^2 - 3r \right)\)[/tex] and simplify it, we can follow these steps:
1. Distribute the [tex]\(-r^2\)[/tex] term:
We need to multiply [tex]\(-r^2\)[/tex] with each term inside the parenthesis [tex]\( (r^2 - 3r) \)[/tex].
[tex]\[
-r^2 \left( r^2 \right) + (-r^2) \left( -3r \right)
\][/tex]
2. Multiply [tex]\(-r^2\)[/tex] by [tex]\( r^2 \)[/tex]:
This gives us:
[tex]\[
-r^2 \cdot r^2 = -r^{4}
\][/tex]
3. Multiply [tex]\(-r^2\)[/tex] by [tex]\(-3r\)[/tex]:
This gives us:
[tex]\[
-r^2 \cdot -3r = 3r^{3}
\][/tex]
4. Combine the results:
Now, combine the results from the distribution steps:
[tex]\[
-r^4 + 3r^3
\][/tex]
5. Factor the combined expression:
We can factor out a common factor of [tex]\( r^3 \)[/tex]:
[tex]\[
-r^4 + 3r^3 = r^3 (3 - r)
\][/tex]
Therefore, the simplified expression is:
[tex]\[
r^3 (3 - r)
\][/tex]
This is the product and the simplified form of the given expression [tex]\(-r^2 \left( r^2 - 3r \right)\)[/tex].
