To find expressions equivalent to \( 12x^2 - 48x + 48 \), we can factor the expression or simplify it.
First, we can factor out the common factor of 12:
\[ 12x^2 - 48x + 48 = 12(x^2 - 4x + 4) \]
Now, notice that the quadratic \( x^2 - 4x + 4 \) can also be factored:
\[ x^2 - 4x + 4 = (x - 2)^2 \]
So, we can write the original expression as:
\[ 12(x - 2)^2 \]
Now, there are a few equivalent expressions we can derive from this factored form. Some examples would include:
- \( 12(x - 2)(x - 2) \) (which is just another way to express \( 12(x - 2)^2 \))
- \( 12(x^2 - 4x + 4) \) (the expression before factoring the quadratic)
- \( 12x^2 - 48x + 48 \) (the original expression)
If you’re given options to choose from, look for two that can be represented as multiples or factorizations of \(12(x - 2)^2\) or the original expression.
If you provide the options, I can help you identify the two correct ones.