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

1 answer

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.