Math Problem Statement

Just answer my question a 2 +ab, a^2 - b^2 a 2 −b 2 , and (a + b)^2 (a+b) 2 ?

Solution

Let's break down the given expressions one by one:

  1. Expression 1: 2+ab2 + ab

    • This is simply the sum of 2 and the product of aa and bb. The expression does not simplify further unless values for aa and bb are provided.
  2. Expression 2: a2b2a^2 - b^2

    • This is a difference of squares, which can be factored as: a2b2=(ab)(a+b)a^2 - b^2 = (a - b)(a + b)
    • This is the factored form of the expression.
  3. Expression 3: (a+b)2(a + b)^2

    • This is a perfect square trinomial, and it expands as: (a+b)2=a2+2ab+b2(a + b)^2 = a^2 + 2ab + b^2
    • This is the expanded form.

So, the expressions are:

  1. 2+ab2 + ab
  2. (ab)(a+b)(a - b)(a + b) (factored form of a2b2a^2 - b^2)
  3. a2+2ab+b2a^2 + 2ab + b^2 (expanded form of (a+b)2(a + b)^2)

Do you need more details or explanations? Here are five related questions:

  1. How do you factor other types of polynomials like a3b3a^3 - b^3?
  2. Can you find the values of aa and bb for specific results of 2+ab2 + ab?
  3. What is the geometric interpretation of a difference of squares?
  4. How do you solve quadratic equations derived from expressions like (a+b)2(a + b)^2?
  5. How can the perfect square formula be applied to solve real-world problems?

Tip: Always check if you can factor or expand expressions to simplify or solve them!

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Math Problem Analysis

Mathematical Concepts

Algebra
Factoring
Expanding Expressions
Difference of Squares
Perfect Square Trinomials

Formulas

a^2 - b^2 = (a - b)(a + b) (Difference of Squares Formula)
(a + b)^2 = a^2 + 2ab + b^2 (Perfect Square Formula)

Theorems

Difference of Squares Theorem
Perfect Square Theorem

Suitable Grade Level

Grades 8-10