(2a-7).jpeg "(2a-7)(2a-7)")
Expanding and Simplifying (2a - 7)(2a - 7)
This expression represents the square of the binomial (2a - 7). We can solve this by using the FOIL method or by recognizing it as a perfect square trinomial.
Using the FOIL Method
- First: Multiply the first terms of each binomial: (2a)(2a) = 4a²
- Outer: Multiply the outer terms of the binomials: (2a)(-7) = -14a
- Inner: Multiply the inner terms of the binomials: (-7)(2a) = -14a
- Last: Multiply the last terms of each binomial: (-7)(-7) = 49
Now, combine the terms: 4a² - 14a - 14a + 49
Simplify: 4a² - 28a + 49
Using the Perfect Square Trinomial Pattern
The perfect square trinomial pattern is: (a - b)² = a² - 2ab + b²
In our case, a = 2a and b = 7. Substituting into the pattern:
(2a - 7)² = (2a)² - 2(2a)(7) + (7)²
Simplifying: 4a² - 28a + 49
Conclusion
Both methods result in the same simplified expression: 4a² - 28a + 49. This demonstrates the power of recognizing patterns in algebra to simplify expressions efficiently.