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Expanding the Square of a Binomial: (2a - 5)^2
This article explores how to expand the expression (2a - 5)^2. This expression represents the square of a binomial, which is a polynomial with two terms.
Understanding the Concept
The square of a binomial means multiplying the binomial by itself. Therefore, (2a - 5)^2 can be written as:
(2a - 5)^2 = (2a - 5)(2a - 5)
Expanding the Expression
To expand the expression, we can use the distributive property (also known as the FOIL method):
- First: Multiply the first terms of each binomial: (2a)(2a) = 4a^2
- Outer: Multiply the outer terms of the binomials: (2a)(-5) = -10a
- Inner: Multiply the inner terms of the binomials: (-5)(2a) = -10a
- Last: Multiply the last terms of each binomial: (-5)(-5) = 25
Now, combine the terms:
4a^2 - 10a - 10a + 25
Simplify by combining like terms:
4a^2 - 20a + 25
Final Result
Therefore, the expanded form of (2a - 5)^2 is 4a^2 - 20a + 25.
Conclusion
Expanding the square of a binomial involves multiplying the binomial by itself and applying the distributive property. By following these steps, we can arrive at the expanded form of the expression. This process is fundamental in algebra and finds applications in various mathematical and scientific fields.