## Expanding the Square of a Trinomial: (-2x + 5y - 3z)^2

This article explores the process of expanding the square of a trinomial, specifically focusing on the expression **(-2x + 5y - 3z)^2**.

### Understanding the Concept

Squaring a trinomial means multiplying the trinomial by itself. In this case, we have:

(-2x + 5y - 3z)^2 = (-2x + 5y - 3z) * (-2x + 5y - 3z)

To expand this, we need to distribute each term of the first trinomial to every term of the second trinomial. This can be done systematically using the **FOIL** method, which is usually applied to binomials, but can be extended to trinomials.

### Applying the FOIL Method

**F**irst terms: (-2x) * (-2x) = 4x^2
**O**uter terms: (-2x) * (5y) = -10xy
**I**nner terms: (-2x) * (-3z) = 6xz
**L**ast terms: (5y) * (5y) = 25y^2

Now we repeat the process with the remaining terms:

**F**irst terms: (5y) * (-2x) = -10xy
**O**uter terms: (5y) * (5y) = 25y^2
**I**nner terms: (5y) * (-3z) = -15yz
**L**ast terms: (-3z) * (-2x) = 6xz
**F**irst terms: (-3z) * (5y) = -15yz
**O**uter terms: (-3z) * (-3z) = 9z^2

Finally, we combine all the terms:

4x^2 - 10xy + 6xz + 25y^2 - 10xy - 15yz + 6xz - 15yz + 9z^2

### Simplifying the Expression

Combining like terms, we get the simplified result:

**4x^2 + 25y^2 + 9z^2 - 20xy + 12xz - 30yz**

### Conclusion

Therefore, the expanded form of (-2x + 5y - 3z)^2 is **4x^2 + 25y^2 + 9z^2 - 20xy + 12xz - 30yz**. This process demonstrates how to expand the square of a trinomial by systematically multiplying each term and simplifying the resulting expression.