Let's find the value of the expression
[tex]\[
444^3 - 443 \times 444 \times 445
\][/tex]
First, denote [tex]\( x = 444 \)[/tex]. Then the expression can be rewritten in terms of [tex]\( x \)[/tex]:
[tex]\[
x^3 - (x-1)x(x+1)
\][/tex]
Looking closely at the term [tex]\( (x-1)x(x+1) \)[/tex], we see it represents the product of three consecutive integers.
Now let's compute each term separately:
1. Compute [tex]\( x^3 \)[/tex]:
[tex]\[
x^3 = 444^3 = 87528384
\][/tex]
2. Compute [tex]\( (x-1) \times x \times (x+1) \)[/tex]:
[tex]\[
443 \times 444 \times 445 = 87527940
\][/tex]
Finally, we subtract the second term from the first:
[tex]\[
444^3 - 443 \times 444 \times 445 = 87528384 - 87527940 = 444
\][/tex]
Thus, the value of the expression [tex]\( 444^3 - 443 \times 444 \times 445 \)[/tex] is [tex]\(\boxed{444}\)[/tex].
So the answer is B) 444.
