Question

question
which of the following is not equivalent to (3x - 12)(x + 4)?
○ 3(x² - 8x + 16)
○ 3(x² - 16)
○ 3x² - 48
○ 3x(x + 4) - 12(x + 4)

Explanation:

Step1: Expand the original expression

First, expand \((3x - 12)(x + 4)\). Using the distributive property (FOIL method):
\[

$$\begin{align*} (3x - 12)(x + 4)&=3x\times x+3x\times4-12\times x-12\times4\\ &=3x^{2}+12x - 12x - 48\\ &=3x^{2}-48 \end{align*}$$

\]

Step2: Analyze Option 1: \(3(x^{2}-8x + 16)\)

Expand \(3(x^{2}-8x + 16)\):
\[
3(x^{2}-8x + 16)=3x^{2}-24x + 48
\]
Compare with the expanded form of the original expression (\(3x^{2}-48\)). These are not the same.

Step3: Analyze Option 2: \(3(x^{2}-16)\)

Expand \(3(x^{2}-16)\):
\[
3(x^{2}-16)=3x^{2}-48
\]
This matches the expanded form of the original expression.

Step4: Analyze Option 3: \(3x^{2}-48\)

This is exactly the expanded form of the original expression, so it is equivalent.

Step5: Analyze Option 4: \(3x(x + 4)-12(x + 4)\)

Factor out \((x + 4)\):
\[
3x(x + 4)-12(x + 4)=(3x - 12)(x + 4)
\]
Which is the original expression, so it is equivalent.

Answer:

\(3(x^{2}-8x + 16)\) (the first option)