%5E2.jpeg "(3n-2m)^2")
Expanding the Square of (3n - 2m)
The expression (3n - 2m)² represents the square of the binomial (3n - 2m). To expand this expression, we can use the following methods:
1. Using the FOIL Method:
The FOIL method stands for First, Outer, Inner, Last, which is a mnemonic device used to remember how to multiply two binomials.
- First: Multiply the first terms of each binomial: (3n) * (3n) = 9n²
- Outer: Multiply the outer terms of the binomials: (3n) * (-2m) = -6nm
- Inner: Multiply the inner terms of the binomials: (-2m) * (3n) = -6nm
- Last: Multiply the last terms of each binomial: (-2m) * (-2m) = 4m²
Finally, combine the terms: 9n² - 6nm - 6nm + 4m² = 9n² - 12nm + 4m²
2. Using the Square of a Difference Formula:
The square of a difference formula states: (a - b)² = a² - 2ab + b²
Applying this to our expression:
- a = 3n
- b = 2m
Therefore, (3n - 2m)² = (3n)² - 2(3n)(2m) + (2m)² = 9n² - 12nm + 4m²
Conclusion:
Both methods lead to the same expanded form of (3n - 2m)², which is 9n² - 12nm + 4m². It's important to note that this expression is a trinomial, meaning it consists of three terms. Understanding how to expand such expressions is crucial in various algebraic operations and problem-solving.