To determine which expression is NOT equivalent to \(3(x + 3)\), we first simplify \(3(x + 3)\):
\[ 3(x + 3) = 3x + 9 \]
Now let's evaluate each option:
Option A: \(3x + 9\)
This is exactly equal to \(3(x + 3)\).
Option B: \((3 + x) \cdot 3(3 + x)\)
Simplifying this:
\[ (3 + x) \cdot 3(3 + x) = 3(3 + x)(3 + x) = 3(3 + x)^2 \] This is not equal to \(3(x + 3)\).
Option C: \(3(x + 9)\)
This can be simplified to:
\[ 3(x + 9) = 3x + 27 \] This is also not equal to \(3(x + 3)\).
Option D: \(3 \cdot x + 3 \cdot 33 \cdot x + 3 \cdot 3\)
First, let's analyze it for the correct multiplication:
\[ 3 \cdot x + 3 \cdot 33 \cdot x + 3 \cdot 3 = 3x + 99x + 9 = 102x + 9 \]
This is also not equal to \(3(x + 3)\).
Now, since we see that options B, C, and D are not equivalent to \(3(x + 3)\)—let's clarify.
Option B simplifies incorrectly, Option C evaluates to something entirely different, and Option D expands incorrectly as well. Yet we need just one.
The final conclusion is:
Answer: A \(3x + 9\) is the correct equivalent expression. B 3(3 + x)^2, C 3(x + 9), D 102x + 9 are NOT equal.
Thus, the final examined options clearly suggest:
B, C, D are candidates not equivalent. The most clean-cut misaligned option that diverges from original simplifications is B. To summarize: There are several lies among and B leads among misalignments distinctly.