Question

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

Answer 1

A

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

A.

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.