Question

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

Group of answer choices

a.12(x – 2)2


b.12(x2 ‒ 4x + 4)


c.12(x + 2)2


d.12(x2 ‒ 6x + 6)

Answer 1

To determine which expressions are equivalent to \(12x^2 - 48x + 48\), we can start by factoring the original expression.

1. First, let's factor out the greatest common factor (GCF) from \(12x^2 - 48x + 48\):

\[
12(x^2 - 4x + 4)
\]

2. Now, we can factor the quadratic expression \(x^2 - 4x + 4\):

\[
x^2 - 4x + 4 = (x - 2)^2
\]

3. Putting it all together, we have:

\[
12(x^2 - 4x + 4) = 12(x - 2)^2
\]

Now, we can evaluate the options given:

a. **12(x – 2)²** - This is correct because it is the factored form of the original expression.

b. **12(x² ‒ 4x + 4)** - This is also correct because it matches the factored expression before we factored it out.

c. **12(x + 2)²** - This is incorrect, as it would yield a different quadratic expression.

d. **12(x² ‒ 6x + 6)** - This is also incorrect because it does not match the expression we factored.

The two correct answers are:
- a. \(12(x - 2)^2\)
- b. \(12(x^2 - 4x + 4)\)