2-answer.jpeg "(2x+5)2 Answer")
Expanding the Square: (2x+5)²
This article delves into the expansion of the expression (2x + 5)², illustrating the process and providing a clear understanding of the outcome.
Understanding the Expression
The expression (2x + 5)² represents the square of the binomial (2x + 5). In simpler terms, it means multiplying the binomial by itself.
Expansion Method
To expand the expression, we apply the FOIL method, which stands for First, Outer, Inner, Last. This method helps us systematically multiply all terms within the parentheses.
- First: Multiply the first terms of each binomial: (2x) * (2x) = 4x²
- Outer: Multiply the outer terms of each binomial: (2x) * (5) = 10x
- Inner: Multiply the inner terms of each binomial: (5) * (2x) = 10x
- Last: Multiply the last terms of each binomial: (5) * (5) = 25
Combining Terms
After applying the FOIL method, we obtain the following expression:
4x² + 10x + 10x + 25
Combining the like terms (10x + 10x), we arrive at the final expanded form:
4x² + 20x + 25
Conclusion
Therefore, the expanded form of (2x + 5)² is 4x² + 20x + 25. This expansion process demonstrates the application of algebraic principles and the importance of understanding binomial squares in simplifying and manipulating expressions.