Question

Which expression represents 625p4−16

when factored completely over the complex numbers?
1.
(25p2+4i)(5p−2i)(5p+2i)
2.
(25p2+4i)(25p2−4i)
3.
(5p−2i)2(5p+2i)2
4.
(5p−2)(5p+2)(5p−2i)(5p+2i)

Answer 1

Correct Answer: 4th Option

The step by step solution is shown below:


`625 p^(4) -16 \\ \\ = (25 p^(2) )^(2) - (4)^(2) \\ \\ =(25 p^(2) +4)(25 p^(2) -4) \\ \\ =[(5p)^(2) + (2)^(2) ][(5p)^(2) - (2)^(2) ] \\ \\ =[(5p)^(2) - (i)^(2) (2)^(2) ][(5p)^(2) - (2)^(2) ] \\ \\ = (5p +2i)(5p-2i)(5p+2)(5p-2)`