(-2x+5y-3z)2 Answer

Jasonbradley

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Jun 16, 2024

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Expanding the Expression (-2x + 5y - 3z)²

This article will demonstrate how to expand the expression (-2x + 5y - 3z)².

Understanding the Concept

The expression (-2x + 5y - 3z)² represents the square of a trinomial. To expand it, we need to multiply the trinomial by itself.

The Expansion

We can expand the expression using the following steps:

1. Rewrite the expression: (-2x + 5y - 3z)² = (-2x + 5y - 3z) * (-2x + 5y - 3z)

2. Apply the distributive property: We need to multiply each term in the first trinomial by each term in the second trinomial. This can be done systematically:

   • -2x * (-2x + 5y - 3z) = 4x² - 10xy + 6xz
   • 5y * (-2x + 5y - 3z) = -10xy + 25y² - 15yz
   • -3z * (-2x + 5y - 3z) = 6xz - 15yz + 9z²

3. Combine like terms: Add together the terms that have the same variables and exponents: 4x² - 10xy + 6xz - 10xy + 25y² - 15yz + 6xz - 15yz + 9z² = 4x² - 20xy + 12xz + 25y² - 30yz + 9z²

Final Result

Therefore, the expanded form of (-2x + 5y - 3z)² is: 4x² - 20xy + 12xz + 25y² - 30yz + 9z²