## 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.**