To find the polynomial [tex]\(D - C\)[/tex], we'll subtract polynomial [tex]\(C\)[/tex] from polynomial [tex]\(D\)[/tex]. Let's denote the given polynomials first:
[tex]\[ C = 3y^2 + 4y + 4 \][/tex]
[tex]\[ D = -7y^2 + 3y - 6 \][/tex]
Now we need to calculate [tex]\(D - C\)[/tex]:
[tex]\[ D - C = (-7y^2 + 3y - 6) - (3y^2 + 4y + 4) \][/tex]
To simplify this, distribute the negative sign through the polynomial [tex]\(C\)[/tex]:
[tex]\[ D - C = -7y^2 + 3y - 6 - 3y^2 - 4y - 4 \][/tex]
Next, combine like terms:
1. Combine the [tex]\(y^2\)[/tex] terms:
[tex]\[ -7y^2 - 3y^2 = -10y^2 \][/tex]
2. Combine the [tex]\(y\)[/tex] terms:
[tex]\[ 3y - 4y = -y \][/tex]
3. Combine the constant terms:
[tex]\[ -6 - 4 = -10 \][/tex]
Putting it all together, we get the resultant polynomial:
[tex]\[ D - C = -10y^2 - y - 10 \][/tex]
Thus, the polynomial [tex]\(D - C\)[/tex] in standard form is:
[tex]\[ \boxed{-10y^2 - y - 10} \][/tex]
