Final answer:
Carina's statement is correct; the expression -4(2x-8) is indeed equivalent to the expression -8x-32 after applying the distributive property.
Step-by-step explanation:
The student has asked if the expression -4(2x-8) is equivalent to the expression -8x-32. To determine this, we need to apply the distributive property to the expression -4(2x-8). According to the distributive property, we can multiply the -4 by each term inside the parentheses, which gives -8x + 32.
However, because we have a negative sign in front of the 4, when we distribute it we must also change the sign of the second term. So it should actually be -8x - 32. Therefore, Carina's statement is correct, and the two expressions are indeed equivalent.