Trouble with this algebra question?

Question

Here's the question 1/2(4-2c)+5c. The answer was 4c+2 but I don't understand how they came up with that answer. I applied the distribute property, reduced the fractions then grouped the like terms. My answer was 1/2+9/2c but I'm told that's wrong.

Here's another question. 10 to the second power minus 8 to the second power in a square root. That's the numerator of a fraction. Then 3 to the second power is the denominator. I'm told 2/3 is the answer but I came up with 2/9 since 3 to the second power is 9 and it didn't look like the 3 was in a square root so I thought I had to just square the 3 which gives me 9.

Answer 1

1/2(4-2c)+5c

multiply the 1/2 into the parans

2 - c + 5c

2 + 4c

√(10² - 8²) / 3²

√(100 - 64) / 9

√(36) / 9

6/9

2/3

.

Answer 2

1/2(4-2c) + 5c  You distribute the 1/2 to just the parenthesis.

2-c + 5c  Then you get 2 + 4c

numerator 10^2 - 8^2 = 6^2 = 6

then take the square root you get 6

denominator  3^2 = 9

fraction is 6/9 which is 2/3