17.

Find the product.

(n3 + 5)(n3 – 5)

n6 – 10n3 + 25

n6 – 125

n6 – 10n3 – 25

n6 – 25

1 answer

To find the product of \((n^3 + 5)(n^3 - 5)\), we can use the difference of squares formula, which states:

\[ (a + b)(a - b) = a^2 - b^2 \]

In this case, \(a = n^3\) and \(b = 5\). Applying the formula, we get:

\[
(n^3 + 5)(n^3 - 5) = (n^3)^2 - 5^2
\]

Now, compute the squares:

\[
(n^3)^2 = n^6
\]
\[
5^2 = 25
\]

Therefore, the expression simplifies to:

\[
n^6 - 25
\]

So, the correct answer is:

\[ n^6 - 25 \]