%5E2.jpeg "(2x-5y)^2")
Expanding the Square of a Binomial: (2x-5y)^2
The expression (2x-5y)^2 represents the square of a binomial, which is a polynomial with two terms. To expand this expression, we can use the following steps:
Understanding the Concept
The square of a binomial is essentially multiplying the binomial by itself:
(2x-5y)^2 = (2x-5y)(2x-5y)
Applying the FOIL Method
The FOIL method is a helpful mnemonic for multiplying binomials:
- First: Multiply the first terms of each binomial.
- Outer: Multiply the outer terms of each binomial.
- Inner: Multiply the inner terms of each binomial.
- Last: Multiply the last terms of each binomial.
Applying this to our expression:
- F: (2x)(2x) = 4x^2
- O: (2x)(-5y) = -10xy
- I: (-5y)(2x) = -10xy
- L: (-5y)(-5y) = 25y^2
Combining Like Terms
Now, we add all the terms together and combine the like terms:
4x^2 - 10xy - 10xy + 25y^2 = 4x^2 - 20xy + 25y^2
Conclusion
Therefore, the expanded form of (2x-5y)^2 is 4x^2 - 20xy + 25y^2. This process highlights the importance of understanding the properties of exponents and the FOIL method when dealing with binomial expansions.