Simplify: (5b - 4c)(5b - 2c)
A 25b ^ 2 + 8c ^ 2
B 10b ^ 2 - 6c ^ 2
C 25b ^ 2 + 30bc + 8c ^ 2
D 25b ^ 2 - 30bc + 8c ^ 2
To simplify the expression (5b - 4c)(5b - 2c), we use the distributive property.
(5b - 4c)(5b - 2c) = 5b(5b) + 5b(-2c) - 4c(5b) - 4c(-2c)
= 25b^2 - 10bc - 20bc + 8c^2
= 25b^2 - 30bc + 8c^2
Therefore, the simplified expression is D) 25b^2 - 30bc + 8c^2.
To simplify the expression (5b - 4c)(5b - 2c), we can use the distributive property.
First, multiply the first terms of each binomial: 5b * 5b = 25b^2.
Next, multiply the outer terms of each binomial: 5b * -2c = -10bc.
Then, multiply the inner terms of each binomial: -4c * 5b = -20bc.
Finally, multiply the last terms of each binomial: -4c * -2c = 8c^2.
Now, combine like terms: -10bc + (-20bc) = -30bc.
Therefore, the simplified expression is:
25b^2 - 30bc + 8c^2.
So the answer is option D: 25b^2 - 30bc + 8c^2.