To simplify the expression [tex]\(-3(x+3)^2 - 3 + 3x\)[/tex], follow these steps:
1. Expand the quadratic term: First, expand [tex]\((x+3)^2\)[/tex]:
[tex]\[
(x+3)^2 = x^2 + 6x + 9
\][/tex]
2. Multiply by -3: Distribute the [tex]\(-3\)[/tex] across the expanded quadratic expression:
[tex]\[
-3 \cdot (x^2 + 6x + 9) = -3x^2 - 18x - 27
\][/tex]
3. Combine like terms: Now add the remaining terms [tex]\(-3\)[/tex] and [tex]\(3x\)[/tex] to the expanded and multiplied result:
[tex]\[
-3x^2 - 18x - 27 - 3 + 3x
\][/tex]
4. Simplify the expression: Combine the linear terms and constant terms:
[tex]\[
-3x^2 - 18x + 3x - 27 - 3 = -3x^2 - 15x - 30
\][/tex]
So, the simplified expression in standard form is:
[tex]\[
-3x^2 - 15x - 30
\][/tex]
Therefore, the correct choice is:
[tex]\[
\boxed{-3 x^2 - 15 x - 30}
\][/tex]
