The expression you've written is:

$A^2 + 2ab$

This is a binomial expression that includes three terms:

• $A^2$, which is the square of $A$,
• $2ab$, which is a product of $2$, $a$, and $b$.

Possible interpretations or applications:

1. Factoring: It seems like part of the expansion of a squared binomial. Specifically, it looks similar to the expansion of $(A + b)^2$, which would be:

   $(A + b)^2 = A^2 + 2Ab + b^2$

   If you compare the two, we see that your expression has $2ab$, but lacks the $b^2$ term. If we assume $b^2$ is missing, it could be part of an incomplete expansion.

2. Algebraic Manipulation: If $A$, $a$, and $b$ are variables, then no further simplification can be done unless you have additional information or equations.

Would you like further elaboration or any specific operations performed with this expression?

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Here are some related questions that might help you dive deeper into the topic:

1. How do you expand the square of a binomial?
2. What is the relationship between $A^2 + 2ab$ and $(A + b)^2$?
3. How can you factor expressions involving $A^2 + 2ab$?
4. What happens if we add a constant term, say $+c$, to $A^2 + 2ab$?
5. How do you complete the square on the expression $A^2 + 2ab$?

Tip: Always check for common patterns when simplifying expressions. Recognizing a perfect square or part of an expanded binomial can save time!