Final answer:
Karla is correct in saying that -2x(4x-3) equals -8x² +6x, as distributing the -2x across the binomial results in a negative times a positive yielding -8x², and a negative times a negative yielding +6x.
Step-by-step explanation:
The student's question revolves around the process of distributing a negative value across a binomial and determining the sign of resulting terms. To clarify who is correct between Kevin and Karla, we distribute the -2x into the parentheses:
-2x(4x-3) = -2x × 4x + (-2x) × (-3)
- For the first term, multiplying -2x by 4x gives us -8x² (because the signs are opposite).
- For the second term, multiplying -2x by -3 gives us +6x (because we're multiplying two numbers with the same negative sign, resulting in a positive sign).
Therefore, Karla is correct: -2x(4x-3) = -8x² +6x.