Step-by-step explanation:
Part A:
can be written as the square of u³, or
. Similarly,
. Hence, we can write this as a difference of two squares by writing it as

Part B:
<h3>Difference of Two Squares</h3>
<u>We can first factor a difference of two squares a² - b² into </u><u>(a+b)(a-b)</u>. Here, <em>a</em> would be u³ and <em>b</em> would be v³.

<h3>Sum and Difference of Two Cubes</h3>
We can factor this further by the use of two special formulas to factor a sum of two cubes and a difference of two cubes. These formulas are as follows:

Since u³ + v³ is a sum of two cubes, let's rewrite it.

Since u³ - v³ is a difference of two cubes, we can rewrite it as well.

Now, let's multiply them together again to get the final factored form.

Part C:
If we want to factor
completely, we can just see that x to the sixth power is just
and 1 to the sixth power is just 1. Hence, x can substitute for <em>u </em>and 1 can substitute for v.

We can repeat this for
, as 64 is just 2 to the sixth power.
