Final answer:
To simplify the given expression, distribute the -4 to each term inside the parentheses and combine like terms.
Step-by-step explanation:
To simplify the expression -4(-25y + 4 + 50y - 8), we need to distribute the -4 to each term inside the parentheses. In the first term, -4 times -25y is 100y. In the second term, -4 times 4 is -16. In the third term, -4 times 50y is -200y. And in the fourth term, -4 times -8 is 32. So, the simplified expression is 100y - 16 - 200y + 32. Combining like terms, we get -100y + 16 + 32, which simplifies to -100y + 48.