Math Problem Statement
Factor the deference of two square
Solution
To factor the difference of two squares, we use the formula:
This formula states that any expression of the form can be factored into the product of two binomials: one with a sum and the other with a difference.
Example:
Consider the expression .
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Identify and :
- Here, is , so .
- is , so .
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Apply the formula:
So, the factorization of is .
Another Example:
Factor the expression .
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Identify and :
- is , so .
- is , so .
-
Apply the formula:
So, the factorization of is .
Do you want details or have any questions? Here are five questions for further exploration:
- How can you recognize the difference of two squares in an algebraic expression?
- Can the difference of two squares be used in simplifying complex algebraic fractions?
- What happens if you attempt to factor the sum of two squares?
- How is the difference of squares used in solving quadratic equations?
- Can the difference of two squares formula be extended to higher powers?
Tip: Always check if an expression can be written in the form of before applying the difference of squares formula.
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Math Problem Analysis
Mathematical Concepts
Algebra
Factorization
Quadratic Equations
Formulas
Difference of squares formula (a^2 - b^2 = (a + b)(a - b))
Theorems
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Suitable Grade Level
Grades 9-12