(2x-%E2%80%93-5y).jpeg "(2x + 5y)(2x – 5y)")
Understanding the Special Product: (2x + 5y)(2x – 5y)
This expression represents a special product known as the difference of squares. Let's break down why this is and how to simplify it.
The Difference of Squares Pattern
The general pattern for the difference of squares is:
(a + b)(a – b) = a² – b²
This pattern arises because when you multiply the two binomials, the middle terms cancel each other out. Let's see how this applies to our example:
Applying the Pattern
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Identify 'a' and 'b': In our expression, (2x + 5y)(2x – 5y):
- a = 2x
- b = 5y
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Apply the pattern:
- a² = (2x)² = 4x²
- b² = (5y)² = 25y²
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Substitute and simplify:
- (2x + 5y)(2x – 5y) = 4x² – 25y²
Conclusion
Therefore, the simplified form of (2x + 5y)(2x – 5y) is 4x² – 25y². Recognizing and applying the difference of squares pattern simplifies the multiplication process and allows for a quicker solution.