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(2x^ 2 +7x+4)-(x^ 2 +3x+2)

2 min read Jun 16, 2024
(2x^ 2 +7x+4)-(x^ 2 +3x+2)

Simplifying Polynomial Expressions: A Step-by-Step Guide

This article will guide you through the process of simplifying the polynomial expression: (2x^2 + 7x + 4) - (x^2 + 3x + 2).

Understanding the Concept

The given expression involves subtracting one polynomial from another. To simplify this, we will use the distributive property and combine like terms.

Steps to Simplify the Expression:

  1. Distribute the Negative Sign:

    • Begin by distributing the negative sign in front of the second parenthesis.
    • This means multiplying each term inside the second parenthesis by -1.
    • The expression becomes: 2x^2 + 7x + 4 - x^2 - 3x - 2

  2. Combine Like Terms:

    • Identify terms with the same variable and exponent (like terms).
    • Combine the x^2 terms: 2x^2 - x^2 = x^2
    • Combine the x terms: 7x - 3x = 4x
    • Combine the constant terms: 4 - 2 = 2

  3. Write the Simplified Expression:

    • Combine the simplified terms to get the final result.
    • The simplified expression is: x^2 + 4x + 2

Conclusion

Therefore, the simplified form of the polynomial expression (2x^2 + 7x + 4) - (x^2 + 3x + 2) is x^2 + 4x + 2. This process demonstrates how to simplify polynomial expressions by using the distributive property and combining like terms.

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