Math Problem Statement

A2+b2+2ab=?

Solution

The given expression is A2+b2+2abA^2 + b^2 + 2ab.

This matches the algebraic identity:
(A+b)2=A2+2ab+b2(A + b)^2 = A^2 + 2ab + b^2

So: A2+b2+2ab=(A+b)2A^2 + b^2 + 2ab = (A + b)^2

Final Answer:

A2+b2+2ab=(A+b)2A^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 (Ab)2(A - b)^2 differ from (A+b)2(A + b)^2?
  2. Can you derive the identity for (A+B+C)2(A + B + C)^2?
  3. How would you expand 2(A2+b2+2ab)2(A^2 + b^2 + 2ab)?
  4. What is the geometric interpretation of (A+b)2(A + b)^2?
  5. How can this formula be applied in solving quadratic equations?

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

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Math Problem Analysis

Mathematical Concepts

Algebra
Algebraic Identities

Formulas

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

Theorems

Expansion of binomials

Suitable Grade Level

Grades 7-9