Question

.

Which expression represents





625p4-16
when factored completely over the complex numbers?

Answer 1

`(5p - 2)(5p + 2)(25 {p}^(2) + 4)`

Explanation:

`625 {p}^(4) - 16 \\ =( 25 {p}^(2)) ^(2) - {4}^(2) \\ = (25 {p}^(2) - 4) (25 {p}^(2) + 4) \\ = \{(5 {p})^(2) - ({2})^(2) \}(25 {p}^(2) + 4) \\ = (5p - 2)(5p + 2)(25 {p}^(2) + 4) \\`