Question

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

Answer 1

Answer:

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

Step-by-step 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:

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

Answer 2

Answer:

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

Step-by-step explanation:

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