Simplify the expression [tex]-3(x+3)^2 - 3 + 3x[/tex]. What is the simplified expression in standard form?

A. [tex]-3x^2 - 18x - 27[/tex]
B. [tex]-3x^2 - 15x - 30[/tex]
C. [tex]-3x^2 + 3x + 6[/tex]
D. [tex]-3x^2 + 3x - 30[/tex]



Answer :

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]