To determine which expressions are equivalent to \(12x^2 - 48x + 48\), we can start by factoring the original expression.
- First, let's factor out the greatest common factor (GCF) from \(12x^2 - 48x + 48\):
\[ 12(x^2 - 4x + 4) \]
- Now, we can factor the quadratic expression \(x^2 - 4x + 4\):
\[ x^2 - 4x + 4 = (x - 2)^2 \]
- 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. \(12(x^2 - 4x + 4)\)
12 answers