(2x-7).jpeg "(2x+7)(2x-7)")
Understanding the Multiplication of (2x+7)(2x-7)
This expression represents the multiplication of two binomials. The key to understanding this multiplication lies in recognizing the pattern it follows:
(a + b)(a - b) = a² - b²
This pattern is known as the difference of squares. Let's break down why it works and how it applies to our expression.
Applying the Difference of Squares
In our expression, (2x+7)(2x-7):
- a = 2x
- b = 7
Therefore, applying the difference of squares pattern:
(2x + 7)(2x - 7) = (2x)² - (7)²
Simplifying the Expression
Now, we can simplify further:
(2x)² - (7)² = 4x² - 49
This is our final simplified expression.
Key Takeaways
- The difference of squares pattern is a valuable tool for quickly multiplying binomials.
- Recognizing this pattern allows us to skip the traditional FOIL method, saving time and effort.
- The simplification process is straightforward, involving only squaring the terms 'a' and 'b' and subtracting them.
By understanding and applying the difference of squares pattern, you can efficiently solve expressions like (2x+7)(2x-7) and streamline your algebraic calculations.