2-solution.jpeg "(-2x+5y-3z)2 Solution")
Expanding (-2x + 5y - 3z)²
This expression represents the square of a trinomial, meaning it's multiplied by itself. To solve it, we'll use the distributive property or, more conveniently, the FOIL method (First, Outer, Inner, Last) combined with the distributive property.
Step 1: Break down the expression
We can rewrite the expression as: (-2x + 5y - 3z) * (-2x + 5y - 3z)
Step 2: Apply FOIL method to the first two terms
- First: (-2x) * (-2x) = 4x²
- Outer: (-2x) * (5y) = -10xy
- Inner: (5y) * (-2x) = -10xy
- Last: (5y) * (5y) = 25y²
This gives us: 4x² - 10xy - 10xy + 25y²
Step 3: Distribute the remaining term
Now we need to distribute the -3z to each term in the first trinomial:
- (-3z) * (-2x) = 6xz
- (-3z) * (5y) = -15yz
- (-3z) * (-3z) = 9z²
Step 4: Combine like terms
Adding all the terms together and combining like terms, we get:
4x² - 20xy + 25y² + 6xz - 15yz + 9z²
Therefore, the expanded form of (-2x + 5y - 3z)² is 4x² - 20xy + 25y² + 6xz - 15yz + 9z².