If x – y = 25 and xy = 444, compute the value of x³ – y³.

The correct option is 48,925.

To find the value of $x^3-y^3$, we can use the algebraic identity for the difference of two cubes:
$x^3-y^3=(x-y)(x^2+xy+y^2)$

We can rewrite the term $x^2+xy+y^2$ using the known expressions $x-y$ and $xy$:
$x^2+xy+y^2=(x^2-2xy+y^2)+3xy={(x-y)}^2+3xy$

Substituting this relation into the expansion for the difference of cubes gives:
$x^3-y^3=(x-y)[{(x-y)}^2+3xy]$

We are given the following values:
• $x-y=25$
• $xy=444$

Now, let's substitute these values step-by-step into the formula:

Step 1: Compute the square of the difference:
${(x-y)}^2={25}^2=625$

Step 2: Compute three times the product:
$3xy=3\times 444=1332$

Step 3: Sum the results of Step 1 and Step 2:
$625+1332=1957$

Step 4: Multiply by the difference $(x-y)$ to get the final answer:
$x^3-y^3=25\times 1957=48925$

Therefore, the value of $x^3-y^3$ is 48,925.