Alright, let's work through this polynomial step by step to express it in standard form.
We start with the given polynomial expression:
[tex]\[
-5 k^2 \left(k^2 - 4k\right)
\][/tex]
To simplify this, we need to distribute [tex]\(-5 k^2\)[/tex] across each term inside the parentheses.
First, multiply [tex]\(-5 k^2\)[/tex] by the first term [tex]\(k^2\)[/tex]:
[tex]\[
-5 k^2 \cdot k^2 = -5 k^4
\][/tex]
Next, multiply [tex]\(-5 k^2\)[/tex] by the second term [tex]\(-4k\)[/tex]:
[tex]\[
-5 k^2 \cdot (-4k) = 20 k^3
\][/tex]
Now, we combine these results to form the polynomial in standard form:
[tex]\[
-5 k^4 + 20 k^3
\][/tex]
So the simplified polynomial in standard form is:
[tex]\[
-5 k^4 + 20 k^3
\][/tex]
