The given expression is $A^2 + b^2 + 2ab$.

This matches the algebraic identity:
$(A + b)^2 = A^2 + 2ab + b^2$

So: $A^2 + b^2 + 2ab = (A + b)^2$

Final Answer:

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

Would you like me to provide a detailed explanation of this step-by-step?

Here are some related questions to deepen your understanding:

1. How does the expansion of $(A - b)^2$ differ from $(A + b)^2$?
2. Can you derive the identity for $(A + B + C)^2$?
3. How would you expand $2(A^2 + b^2 + 2ab)$?
4. What is the geometric interpretation of $(A + b)^2$?
5. How can this formula be applied in solving quadratic equations?

Tip: Memorizing algebraic identities like $(A + b)^2$ and $(A - b)^2$ simplifies many problems in algebra.