(2x^2+3y^2-z^2)-(x^2-y^2-z^2)+(4x^2-3y^2)

3 min read Jun 16, 2024

Simplifying Algebraic Expressions: A Step-by-Step Guide

This article will guide you through the process of simplifying the algebraic expression: (2x^2 + 3y^2 - z^2) - (x^2 - y^2 - z^2) + (4x^2 - 3y^2).

Understanding the Expression

Before we start simplifying, let's break down the expression. It involves:

Variables: x, y, and z, representing unknown values.
Coefficients: Numbers multiplying the variables (2, 3, -1, 1, 4, -3).
Exponents: Powers indicating how many times a variable is multiplied by itself (x^2, y^2, z^2).
Parentheses: Grouping terms together.

The Simplification Process

Remove the parentheses: We begin by distributing the negative sign in front of the second set of parentheses.
- (2x^2 + 3y^2 - z^2) - (x^2 - y^2 - z^2) + (4x^2 - 3y^2) =
- 2x^2 + 3y^2 - z^2 - x^2 + y^2 + z^2 + 4x^2 - 3y^2
Combine like terms: We combine terms with the same variable and exponent.
- (2x^2 - x^2 + 4x^2) + (3y^2 + y^2 - 3y^2) + (-z^2 + z^2)
Simplify: We perform the arithmetic operations within each group.
- 5x^2 + y^2

Result

The simplified expression is 5x^2 + y^2.

Key Takeaways

Order of operations: Follow the order of operations (PEMDAS/BODMAS) when simplifying.
Distributing negatives: Remember to distribute a negative sign when removing parentheses.
Combining like terms: Combine terms with the same variable and exponent.

This example demonstrates how to simplify algebraic expressions by applying basic algebraic rules. Understanding these rules is crucial for working with polynomials and other mathematical concepts.