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:

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