Which of the following is the correct factorization of the polynomial below?
p3 - 125q3

A

Step-by-step explanation:

p³ - 125q³ ← is a difference of cubes and factors in general as

a³ - b³ = (a - b)(a² + ab + b³)

here a = p and b = 5q, hence

p³ - (5q)³

= (p - 5q)(p² + ( 5q)p + (- 5q)² )

= (p - 5q)(p² + 5pq + 25q²) → A

Step-by-step explanation:

The given expression is

This is the difference of two perfect cubes, which can be factored using the following formula

Where and , because the cubic root of 125 is 5.

Therefore, the right answer is A, because it shows the correct factored form of the given difference.