Final answer:
To factor b²-c²-10(b-c), use the difference of squares formula to get (b+c-10)(b-c). To factor x²-7x+7y-y², group the terms and factor each group to get x(x-7) - y(7-y).
Step-by-step explanation:
To factor these problems, let's look at them one at a time:
1. To factor b²-c²-10(b-c), we can use the difference of squares formula. The formula states that a² - b² = (a + b)(a - b). Applying this to our problem, we have (b+c)(b-c) - 10(b-c). Now we can factor out the common binomial (b-c) to get (b+c-10)(b-c).
2. To factor x²-7x+7y-y², we can group the terms. Group the first two terms and the last two terms: (x²-7x) + (7y-y²). Now we can factor each group. For the first group, we can factor out x to get x(x-7). For the second group, we can factor out -y to get -y(7-y). Combining these factors, we have x(x-7) - y(7-y).