%5E2-simplify.jpeg "(2x-5)^2 Simplify")
Simplifying (2x - 5)^2
The expression (2x - 5)^2 represents the square of the binomial (2x - 5). To simplify it, we can use the FOIL method or the square of a binomial formula.
Using the FOIL Method
FOIL stands for First, Outer, Inner, Last, and helps us multiply two binomials.
- First: Multiply the first terms of each binomial: (2x) * (2x) = 4x²
- Outer: Multiply the outer terms of the binomials: (2x) * (-5) = -10x
- Inner: Multiply the inner terms of the binomials: (-5) * (2x) = -10x
- Last: Multiply the last terms of each binomial: (-5) * (-5) = 25
Now, combine the terms: 4x² - 10x - 10x + 25
Finally, simplify by combining like terms: 4x² - 20x + 25
Using the Square of a Binomial Formula
The square of a binomial formula states that: (a + b)² = a² + 2ab + b²
Applying this to our expression, we have:
(2x - 5)² = (2x)² + 2(2x)(-5) + (-5)²
Simplifying, we get:
4x² - 20x + 25
Conclusion
Both methods lead to the same simplified expression: 4x² - 20x + 25. Choose the method you find easier and more comfortable to use. Remember, understanding the concepts behind the methods is key to simplifying expressions confidently.