To factorize the expression A² - b² - a - b, we can use the difference of squares formula.
The difference of squares formula states that A² - b² can be factored as (A + b)(A - b).
So, applying this formula to our expression, we have:
A² - b² - a - b = (A + b)(A - b) - a - b.
Now, we can combine like terms by distributing (A + b) to (A - b):
(A + b)(A - b) - a - b = A(A - b) + b(A - b) - a - b.
Next, we can further simplify by factoring out the common factor (A - b):
A(A - b) + b(A - b) - a - b = (A + b)(A - b) - (a + b).
Therefore, the fully factorized expression is:
(A + b)(A - b) - (a + b).
Please note that if you have specific values for A, b, a, and b, you can substitute those values into the expression to simplify further.