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The simplified expression is
.
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Mind Expander
To simplify the expression
, we can start by rewriting it for clarity:
Now, we can expand the first two terms:
-
For the first term
: -
For the second term
: -
The third term is
.
Now, let’s combine all these terms and group them properly. To handle the expression more efficiently, we can express them with a common denominator which is
:
-
First term to common denominator:
-
Second term:
-
Third term:
-
The
term expressed with the common denominator:
Now we have:
After combining the numerators, simplify and cancel terms wherever possible. Let’s analyze the resulting polynomial carefully to find if it can be further simplified or has a pattern.
Feel free to plug in specific values for
,
, and
for practical numeric exploration or further refinements. This combinatorial style of working through each component lets us see how everything interacts algebraically, leading us toward a clear and simplified answer!