Question

Which expressions are equivalent to 12x2 – 48x + 48? Select TWO correct answers.

Group of answer choices

12(x – 2)2

12(x + 2)2

12(x2 ‒ 4x + 4)

12(x2 ‒ 6x + 6)

Answer 1

To determine which expressions are equivalent to the quadratic expression \( 12x^2 - 48x + 48 \), we can factor the original expression or manipulate the given options.

First, we can factor \( 12x^2 - 48x + 48 \):

1. Factor out 12 from the expression:
\[
12(x^2 - 4x + 4)
\]

2. Now, \( x^2 - 4x + 4 \) can be factored further as:
\[
x^2 - 4x + 4 = (x - 2)^2
\]

So we have:
\[
12(x^2 - 4x + 4) = 12(x - 2)^2
\]

From this, we find that:
- The expression \( 12(x - 2)^2 \) is indeed equivalent to \( 12x^2 - 48x + 48 \).
- The expression \( 12(x^2 - 4x + 4) \) is just a different representation and is also equivalent to the original expression.

Now we can analyze the answer choices:

1. **12(x – 2)²**: Equivalent (as we derived).
2. **12(x + 2)²**: Not equivalent.
3. **12(x² ‒ 4x + 4)**: Equivalent (as we derived).
4. **12(x² ‒ 6x + 6)**: Not equivalent.

Therefore, the two correct answers are:
- 12(x – 2)²
- 12(x² ‒ 4x + 4)