Certainly! Let's simplify the given expression step-by-step to write it as a polynomial in standard form.
We start with the expression:
[tex]\[ 3h (-h^2 + 2h - 1) \][/tex]
First, distribute [tex]\( 3h \)[/tex] across each term inside the parentheses:
1. Multiply [tex]\( 3h \)[/tex] by [tex]\( -h^2 \)[/tex]:
[tex]\[ 3h \cdot (-h^2) = -3h^3 \][/tex]
2. Multiply [tex]\( 3h \)[/tex] by [tex]\( 2h \)[/tex]:
[tex]\[ 3h \cdot 2h = 6h^2 \][/tex]
3. Multiply [tex]\( 3h \)[/tex] by [tex]\( -1 \)[/tex]:
[tex]\[ 3h \cdot (-1) = -3h \][/tex]
Now, combine all these results to form the polynomial:
[tex]\[ -3h^3 + 6h^2 - 3h \][/tex]
Therefore, the expression [tex]\( 3h (-h^2 + 2h - 1) \)[/tex] simplifies to:
[tex]\[ -3h^3 + 6h^2 - 3h \][/tex]
So, the polynomial in standard form is:
[tex]\[ -3h^3 + 6h^2 - 3h \][/tex]
