The rule of square factoring, specifically the difference of squares, states that an expression in the form a² - b² can be factored into (a + b)(a - b).
In simpler terms, if you have a perfect square minus another perfect square, you can factor it into two binomials: one with the sum of the square roots of the terms, and the other with the difference of the square roots of the terms.
Let's break it down:
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Identify perfect squares: Ensure that you have two terms, both of which are perfect squares (meaning they can be obtained by squaring some value).
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Recognize the subtraction: Verify that the terms are being subtracted. This is crucial because this rule applies to the difference of squares.
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Apply the formula: If you meet the above criteria, you can use the formula a² - b² = (a + b)(a - b).
Example:
Factor x² - 9
- Identify perfect squares: x² is the square of x, and 9 is the square of 3.
- Recognize subtraction: We have x² minus 9.
- Apply the formula: Therefore, x² - 9 = (x + 3)(x - 3).
Another Example:
Factor 4y² - 25
- Identify perfect squares: 4y² is the square of 2y, and 25 is the square of 5.
- Recognize subtraction: We have 4y² minus 25.
- Apply the formula: Therefore, 4y² - 25 = (2y + 5)(2y - 5).
This rule provides a shortcut for factoring expressions in the form of a difference of squares, saving time and effort compared to other factoring methods.
