Final answer:
The expression 64f - 64g + 96 can be factored correctly as 8(8f - 8g + 12). Option B is the correct factorization for the given expression.
Step-by-step explanation:
The question asks to factor the expression 64f - 64g + 96. To factor this expression, we look for the greatest common factor (GCF) that divides each term. Looking at the coefficients (64, 64, 96), we can see that the GCF is 64. Therefore, we can factor the expression as follows:
64f - 64g + 96 = 64(f - g + 1.5). However, this is not one of the answer choices provided.
To match the answer choices, we examine each provided option for correctness.
- Option A suggests the expression can be factored to 64(f - g + 2). If we distribute 64 back into the parentheses, we get the original expression: 64f - 64g + 128. This is close, but the constant term is incorrect.
- Option B: 8(8f - 8g + 12) also needs to be verified. Multiplying 8 by each term in the parentheses gives us 64f - 64g + 96, which is the original expression. Therefore, Option B is the correct factorization.
- Options C and D can be checked in a similar fashion but ruling them out after finding the correct answer is more efficient.
Therefore, the equivalent expression by factoring the given expression is Option B: 8(8f - 8g + 12).