27a4b7 (A-1)3
----------- • ------------ = ?
3a2-6a-3 9ab
3a^2-6a-3 = 3(a-1)^2, so we end up with
27a^4b^7(a-1) / 27ab = a^3b^6/(a-1)
To simplify the expression (A-1)3, we evaluate it further by distributing the 3 to both terms inside the parentheses:
(A-1)3 = 3A - 3
So, the expression becomes:
27a4b7
----------
3a2-6a-3
----------
9ab
To simplify this expression, we need to find any common factors that we can cancel out. Let's break it down step by step:
Step 1: Simplify the numerator.
The numerator, 27a4b7, cannot be simplified further.
Step 2: Simplify the denominator.
To simplify the denominator, we factor out common terms from each term:
3a2-6a-3 = 3(a2-2a-1)
The expression becomes:
27a4b7
---------
3(a2-2a-1)
---------
9ab
Step 3: Simplify the denominator.
Since there are no common factors in the denominator that can be canceled with the numerator, we can leave it as it is.
So, the simplified expression is:
27a4b7
---------
3(a2-2a-1)
---------
9ab
To find the answer to the expression, we divide the numerator by the denominator:
27a4b7
--------- = 9a3b6
3(a2-2a-1)
Therefore, the simplified expression is 9a3b6.