To simplify the expression [tex]\(-3(x+3)^2 - 3 + 3x\)[/tex] and present it in standard form, we can follow these steps:
1. Expand [tex]\((x+3)^2\)[/tex]:
The term [tex]\((x+3)^2\)[/tex] can be expanded using the binomial formula:
[tex]\[
(x+3)^2 = x^2 + 6x + 9
\][/tex]
So, replace [tex]\((x+3)^2\)[/tex] with this expanded form:
[tex]\[
-3(x^2 + 6x + 9) - 3 + 3x
\][/tex]
2. Distribute the [tex]\(-3\)[/tex] across the terms inside the parentheses:
Distribute [tex]\(-3\)[/tex] through [tex]\(x^2 + 6x + 9\)[/tex]:
[tex]\[
-3(x^2 + 6x + 9) = -3x^2 - 18x - 27
\][/tex]
Now, plug this result back into the expression:
[tex]\[
-3x^2 - 18x - 27 - 3 + 3x
\][/tex]
3. Combine like terms:
Combine the constants and the linear terms:
[tex]\[
-3x^2 - 18x + 3x - 27 - 3
\][/tex]
Simplify by combining [tex]\(-18x\)[/tex] and [tex]\(3x\)[/tex]:
[tex]\[
-18x + 3x = -15x
\][/tex]
Combine the constants [tex]\(-27\)[/tex] and [tex]\(-3\)[/tex]:
[tex]\[
-27 - 3 = -30
\][/tex]
So, the expression simplifies to:
[tex]\[
-3x^2 - 15x - 30
\][/tex]
4. Conclusion:
The given expression [tex]\(-3(x+3)^2 - 3 + 3x\)[/tex] simplifies to the standard form:
[tex]\[
-3x^2 - 15x - 30
\][/tex]
Thus, the correct answer is:
[tex]\[
\boxed{-3x^2 - 15x - 30}
\][/tex]
