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:
-
Expression 1:
- This is simply the sum of 2 and the product of and . The expression does not simplify further unless values for and are provided.
-
Expression 2:
- This is a difference of squares, which can be factored as:
- This is the factored form of the expression.
-
Expression 3:
- This is a perfect square trinomial, and it expands as:
- This is the expanded form.
So, the expressions are:
- (factored form of )
- (expanded form of )
Do you need more details or explanations? Here are five related questions:
- How do you factor other types of polynomials like ?
- Can you find the values of and for specific results of ?
- What is the geometric interpretation of a difference of squares?
- How do you solve quadratic equations derived from expressions like ?
- 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
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