(2a-5)-answer.jpeg "(2a-5)(2a-5) Answer")
Expanding the Expression (2a - 5)(2a - 5)
This expression represents the squaring of a binomial, specifically (2a - 5). To find the answer, we can use the FOIL method or the square of a binomial pattern.
Using the FOIL Method
FOIL stands for First, Outer, Inner, Last. It's a systematic way to multiply binomials:
- First: Multiply the first terms of each binomial: (2a) * (2a) = 4a²
- Outer: Multiply the outer terms: (2a) * (-5) = -10a
- Inner: Multiply the inner terms: (-5) * (2a) = -10a
- Last: Multiply the last terms: (-5) * (-5) = 25
Now, combine all the terms: 4a² - 10a - 10a + 25
Simplify by combining the like terms: 4a² - 20a + 25
Using the Square of a Binomial Pattern
The square of a binomial pattern states: (a - b)² = a² - 2ab + b²
In our case, a = 2a and b = 5. Applying the pattern:
(2a - 5)² = (2a)² - 2(2a)(5) + 5²
Simplifying: 4a² - 20a + 25
Conclusion
Both methods result in the same answer: 4a² - 20a + 25. This is the expanded form of the expression (2a - 5)(2a - 5).