(3m-3n%2B2).jpeg "(3m+2n-4)(3m-3n+2)")
Expanding the Expression (3m + 2n - 4)(3m - 3n + 2)
This article will guide you through the process of expanding the expression (3m + 2n - 4)(3m - 3n + 2). We will use the FOIL method and demonstrate the step-by-step solution.
Understanding FOIL
FOIL is a mnemonic acronym that stands for First, Outer, Inner, Last. It's a simple way to remember how to multiply two 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.
Expanding the Expression
Step 1: Apply the FOIL method:
- First: (3m)(3m) = 9m²
- Outer: (3m)(-3n) = -9mn
- Inner: (2n)(3m) = 6mn
- Last: (2n)(-3n) = -6n²
Step 2: Multiply the terms of the first binomial by the constant term in the second binomial:
- (3m)(2) = 6m
- (2n)(2) = 4n
- (-4)(2) = -8
Step 3: Combine all the terms:
9m² - 9mn + 6mn - 6n² + 6m + 4n - 8
Step 4: Simplify by combining like terms:
9m² - 3mn - 6n² + 6m + 4n - 8
Final Result
Therefore, the expanded form of the expression (3m + 2n - 4)(3m - 3n + 2) is 9m² - 3mn - 6n² + 6m + 4n - 8.