(v) (-2x+5y-3z)^(2)

3 min read Jun 16, 2024

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

First terms: (-2x) * (-2x) = 4x^2 Outer terms: (-2x) * (5y) = -10xy Inner terms: (-2x) * (-3z) = 6xz Last terms: (5y) * (5y) = 25y^2

Now we repeat the process with the remaining terms:

First terms: (5y) * (-2x) = -10xy Outer terms: (5y) * (5y) = 25y^2 Inner terms: (5y) * (-3z) = -15yz Last terms: (-3z) * (-2x) = 6xz First terms: (-3z) * (5y) = -15yz Outer 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.