%5E2.jpeg "(3x-6y)^2")
Expanding the Square of a Binomial: (3x - 6y)²
In algebra, expanding a binomial squared involves multiplying the binomial by itself. In this case, we are dealing with the expression (3x - 6y)².
Understanding the Process
To expand this expression, we can apply the FOIL method or the square of a difference formula.
- FOIL stands for First, Outer, Inner, Last. It involves multiplying each term of the first binomial by each term of the second binomial.
- Square of a difference formula states: (a - b)² = a² - 2ab + b²
Expanding using FOIL
- First: (3x) * (3x) = 9x²
- Outer: (3x) * (-6y) = -18xy
- Inner: (-6y) * (3x) = -18xy
- Last: (-6y) * (-6y) = 36y²
Now, combine the terms: 9x² - 18xy - 18xy + 36y²
Simplify the expression: 9x² - 36xy + 36y²
Expanding using the Formula
Applying the square of a difference formula:
- a²: (3x)² = 9x²
- 2ab: 2 * (3x) * (-6y) = -36xy
- b²: (-6y)² = 36y²
Combine the terms: 9x² - 36xy + 36y²
Conclusion
Both methods lead to the same expanded form: 9x² - 36xy + 36y². This is the simplified form of (3x - 6y)². Remember, these methods are applicable to expanding any binomial squared.