Final answer:
The only expression equivalent to -2/5(15-20d)5c is option B) -2c (15-20d), which simplifies to -30c + 40cd, matching the original expression when distributed and multiplied.
Step-by-step explanation:
The expressions equivalent to -2/5(15-20d)5c need to be identified. First, distribute the -2/5 across the parentheses: -2/5 × 15 yields -6, and -2/5 × -20d yields 8d. Then multiply these results by 5c to get -6 × 5c = -30c and 8d × 5c = 40cd. Combined, the expression simplifies to -30c + 40cd.
Now we need to match this result with the given options:
- A) 2c(15-20d) simplifies to 30c - 40cd which is incorrect due to the positive sign.
- B) -2c (15-20d) simplifies to -30c + 40cd which is correct.
- C) 2c(3-4d) simplifies to 6c - 8cd which is not equivalent when considering the overall factor.
- D) -2c(3-4d) simplifies to -6c + 8cd which again is not equivalent due to the different factor.
Therefore, the only expression equivalent to -2/5(15-20d)5c given the options is B) -2c (15-20d).