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.

by definition, an arc subtended by a central angle of some given measure has the same measure. so .