Why do difference of squares partial fractions have to be decomposed this way?

Question

Why do you have to factor out $-1$ here?

$$\frac{2000}{(10-h)(10+h)}$$$$=\frac{A}{10-h}+\frac{B}{10+h}$$

Decomposing this finds A annd B to be 100, which is wrong. Symbolab and Wolfram Alpha factor out $-1$ from $(10+h)(10-h)$ before separation. I can't see why...

Answer 1

A method which should work :

$A/(10-h) + B/(10+h) = 2000/(10-h)(10+h) $

Multiply both sides by (10-h)(10+h)

$2000 = A(10+h) + B(10-h)$

Regroup the terms :

$2000 = 10A + Ah +10B -Bh = (A-B)h +10A + 10B$

This equation will be true if A-B = 0 and 10A + 10B = 2000

A = B so 20A = 2000

A = B = 100 is the answer.