The difference of two squares formula allows factoring an expression where one perfect square is subtracted from another perfect square. According to the provided reference, the formula is expressed as follows:
The Difference of Two Squares Formula
The formula, which represents a significant factoring technique in algebra, is:
A² - B² = (A + B) (A - B)
Explanation
This formula states that if you have an expression in the form of A squared minus B squared, it can be factored into two binomials: one is the sum of A and B (A + B), and the other is the difference of A and B (A - B).
Examples
Here are a few examples to illustrate how to use the difference of two squares formula:
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Example 1: Factor x² - 9
- Recognize that x² is the square of x and 9 is the square of 3 (3² = 9).
- Apply the formula: x² - 9 = (x + 3) (x - 3)
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Example 2: Factor 4y² - 25
- Recognize that 4y² is the square of 2y and 25 is the square of 5.
- Apply the formula: 4y² - 25 = (2y + 5) (2y - 5)
How it Works
The formula works because when you expand the factored form (A + B)(A - B), you get:
(A + B)(A - B) = A² - AB + AB - B² = A² - B²
The middle terms (-AB and +AB) cancel each other out, leaving you with the difference of two squares.
Importance
The difference of two squares formula is a valuable tool for:
- Factoring quadratic expressions
- Simplifying algebraic expressions
- Solving equations
- Working with polynomial expressions
By recognizing and applying this formula, many algebraic problems can be solved more efficiently.
