Question

Which of the following is the correct factorization of the polynomial below? p^3-125q^3

Answer 1

(p-5q)(p^2+5pq+25q^2)

Explanation:

ap3x

Answer 2

`(p -5q)(p^(2)+5pq+25q^2})`

Explanation:

The given expression is:

`p^(3)-125q^3`

The related formula is:

`a^3-b^3=(a-b)(a^(2)+ab+b^(2))`

We can transform the given expression in the form of a³ - b³ as shown below:

`p^(3)-125q^3\\= p^(3) - 5^(3)q^(3)\\=p^(3)-(5q)^(3)`

Now here a = p and b = 5q. Using the above factorization, we get:

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