Answer:
A.
Step-by-step explanation:
The given expression is
[tex]p^{3}-125q^{3}[/tex]
This is the difference of two perfect cubes, which can be factored using the following formula
[tex]a^{3} -b^{3} =(a-b)(a^{2}+ab+b^{2} )[/tex]
Where [tex]a=p[/tex] and [tex]b=5q[/tex], because the cubic root of 125 is 5.
[tex]p^{3}-125q^{3}=(p-5q)(p^{2}+(p)(5q)+(5q)^{2} )\\p^{3}-125q^{3}=(p-5q)(p^{2}+5pq+25q^{2} )[/tex]
Therefore, the right answer is A, because it shows the correct factored form of the given difference.
