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(5x^2-3)+(2x^2-3x^3)

2 min read Jun 16, 2024
(5x^2-3)+(2x^2-3x^3)

Simplifying the Expression: (5x^2 - 3) + (2x^2 - 3x^3)

This article will guide you through the process of simplifying the algebraic expression (5x^2 - 3) + (2x^2 - 3x^3).

Understanding the Expression

The expression consists of two binomials:

  • (5x^2 - 3)
  • (2x^2 - 3x^3)

These binomials are being added together.

Simplifying the Expression

To simplify the expression, we'll combine like terms:

  1. Identify like terms:

    • x^3 terms: -3x^3
    • x^2 terms: 5x^2 and 2x^2
    • Constant terms: -3

  2. Combine like terms:

    • x^3 terms: -3x^3
    • x^2 terms: 5x^2 + 2x^2 = 7x^2
    • Constant terms: -3

  3. Write the simplified expression:

The simplified expression is -3x^3 + 7x^2 - 3.

Key Points

  • Like terms have the same variable raised to the same power.
  • When adding like terms, we only add the coefficients.
  • The order of terms in a polynomial doesn't affect its value, but it's generally written in descending order of exponents.

By following these steps, we have successfully simplified the expression (5x^2 - 3) + (2x^2 - 3x^3).

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