Question

simplify the expression $-3(x + 3)^2 - 3 + 3x$. what is the simplified expression in standard form?\
\bigcirc $-3x^2 - 18x - 27$\
\bigcirc $-3x^2 - 15x - 30$\
\bigcirc $-3x^2 + 3x + 6$\
\bigcirc $-3x^2 + 3x - 30$

Explanation:

Step1: Expand \((x + 3)^2\)

Using the formula \((a + b)^2 = a^2 + 2ab + b^2\), where \(a = x\) and \(b = 3\), we get \((x + 3)^2 = x^2 + 6x + 9\).

Step2: Multiply by \(-3x\) (Wait, no, the original expression is \(-3(x + 3)^2 - 3 + 3x\). So first multiply \(-3\) with \((x + 3)^2\))

\(-3(x^2 + 6x + 9)=-3x^2 - 18x - 27\)

Step3: Add the remaining terms \(-3 + 3x\)

\(-3x^2 - 18x - 27 - 3 + 3x\)
Combine like terms: \(-3x^2+(-18x + 3x)+(-27 - 3)=-3x^2 - 15x - 30\)

Answer:

\(-3x^2 - 15x - 30\) (Corresponding to the option with this expression)