(2x-7y).jpeg "(2x+7y)(2x-7y)")
Factoring the Difference of Squares: (2x + 7y)(2x - 7y)
This expression is a classic example of the difference of squares pattern. Here's how to factor it:
Understanding the Pattern
The difference of squares pattern is a fundamental concept in algebra:
a² - b² = (a + b)(a - b)
This pattern allows us to factor expressions where we have two perfect squares separated by a minus sign.
Applying the Pattern
Let's break down the expression (2x + 7y)(2x - 7y) to see how it fits the pattern:
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Identify the squares: Notice that both terms in the expression are squares:
- (2x)² = 4x²
- (7y)² = 49y²
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Recognize the subtraction: There's a minus sign between the squares.
Now, we can directly apply the difference of squares pattern:
(2x + 7y)(2x - 7y) = (2x)² - (7y)²
Finally, we simplify:
**(2x)² - (7y)² = ** 4x² - 49y²
Conclusion
Therefore, the factored form of (2x + 7y)(2x - 7y) is 4x² - 49y². This pattern is crucial for simplifying expressions and solving equations in algebra.