Math Problem Statement

(a+b)(a-b)

Solution

The expression (a+b)(ab)(a + b)(a - b) is a product of two binomials. This is a difference of squares formula, which can be expanded as:

(a+b)(ab)=a2b2(a + b)(a - b) = a^2 - b^2

Explanation:

  • The product of the sum and difference of the same two terms aa and bb results in the difference between their squares.
  • In this case:
    • a×a=a2a \times a = a^2
    • b×b=b2-b \times b = -b^2

Thus, (a+b)(ab)(a + b)(a - b) simplifies to a2b2a^2 - b^2.

Would you like more details or have any questions?

Related Questions:

  1. How do you apply the difference of squares formula to (x+3)(x3)(x + 3)(x - 3)?
  2. What is the result of (2a+3b)(2a3b)(2a + 3b)(2a - 3b)?
  3. How does the difference of squares relate to factoring quadratic expressions?
  4. Can you solve the equation (a+b)(ab)=0(a + b)(a - b) = 0 for aa and bb?
  5. How does the difference of squares apply to complex numbers?

Tip:

When recognizing patterns in algebraic expressions, such as the difference of squares, it becomes easier to factor or expand them quickly.

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Math Problem Analysis

Mathematical Concepts

Algebra
Binomial Theorem
Difference of Squares

Formulas

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Theorems

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Suitable Grade Level

Grades 9-12