Question

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

Answer 1

Answer:

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

Answer 2

Answer:

A.

Step-by-step explanation:

The given expression is

$p^{3}-125q^{3}$

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

$a^{3} -b^{3} =(a-b)(a^{2}+ab+b^{2} )$

Where $a=p$ and $b=5q$, because the cubic root of 125 is 5.

$p^{3}-125q^{3}=(p-5q)(p^{2}+(p)(5q)+(5q)^{2} )\\p^{3}-125q^{3}=(p-5q)(p^{2}+5pq+25q^{2} )$

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