Math Problem Statement

(A+b) (b+a)

Solution

The expression (A+b)(b+A)(A + b)(b + A) can be expanded using the distributive property (also known as the FOIL method for binomials):

Steps:

  1. Multiply the first terms: Ab=AbA \cdot b = Ab
  2. Multiply the outer terms: AA=A2A \cdot A = A^2
  3. Multiply the inner terms: bb=b2b \cdot b = b^2
  4. Multiply the last terms: bA=Abb \cdot A = Ab

Combine like terms:

(A+b)(b+A)=A2+Ab+Ab+b2(A + b)(b + A) = A^2 + Ab + Ab + b^2

=A2+2Ab+b2= A^2 + 2Ab + b^2

Final result:

(A+b)(b+A)=A2+2Ab+b2(A + b)(b + A) = A^2 + 2Ab + b^2

Would you like a detailed explanation of any step?

Related Questions:

  1. What is the difference between expanding and factoring an expression?
  2. How do we apply the distributive property to larger polynomials?
  3. What is the geometric interpretation of the expansion of binomials?
  4. How does the FOIL method extend to trinomials?
  5. Can you demonstrate this expansion using specific values for AA and bb?

Tip: Always check for like terms when simplifying expanded polynomials!

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Math Problem Analysis

Mathematical Concepts

Algebra
Polynomial Expansion
Distributive Property

Formulas

Distributive Property: (x + y)(a + b) = xa + xb + ya + yb
Combining Like Terms

Theorems

Commutative Property of Addition and Multiplication

Suitable Grade Level

Grades 8-10