(2a-1)%2B(a-7)(a%2B7).jpeg "(2a+1)(2a-1)+(a-7)(a+7)")
Simplifying the Expression: (2a+1)(2a-1)+(a-7)(a+7)
This article will guide you through simplifying the algebraic expression: (2a+1)(2a-1)+(a-7)(a+7).
Understanding the Patterns
The given expression contains two multiplications of binomials, each resembling a specific pattern:
- (2a+1)(2a-1): This is a difference of squares pattern. It follows the formula: (x+y)(x-y) = x² - y²
- (a-7)(a+7): This is also a difference of squares pattern, following the same formula.
Applying the Patterns
Let's apply the difference of squares pattern to simplify the expression:
- (2a+1)(2a-1): Using the formula, this becomes (2a)² - (1)² = 4a² - 1
- (a-7)(a+7): Applying the formula, this becomes (a)² - (7)² = a² - 49
Now our expression is simplified to: 4a² - 1 + a² - 49
Combining Like Terms
The final step is to combine the like terms:
- 4a² + a² = 5a²
- -1 - 49 = -50
Therefore, the simplified form of the expression is: 5a² - 50
Conclusion
By recognizing the difference of squares patterns and applying them to the expression, we were able to simplify it to 5a² - 50. This example highlights the importance of understanding and applying algebraic patterns to simplify complex expressions.