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(9x^3+2x^2-5x+4)-(5x^3-7x+4)

2 min read Jun 16, 2024
(9x^3+2x^2-5x+4)-(5x^3-7x+4)

Simplifying Polynomial Expressions: (9x^3+2x^2-5x+4)-(5x^3-7x+4)

This article will guide you through the process of simplifying the polynomial expression: (9x^3+2x^2-5x+4)-(5x^3-7x+4).

Understanding the Basics

Before we begin, let's recall some key concepts:

  • Polynomials: Expressions consisting of variables and constants combined using addition, subtraction, and multiplication, with non-negative integer exponents.
  • Simplifying Polynomials: Combining like terms to write the polynomial in its most concise form.
  • Like Terms: Terms that have the same variable(s) raised to the same power.

The Steps to Simplify

  1. Distribute the negative sign: The minus sign in front of the second parenthesis means we multiply each term inside the parenthesis by -1:

    (9x^3+2x^2-5x+4) + (-1 * 5x^3) + (-1 * -7x) + (-1 * 4)

  2. Simplify:

    9x^3 + 2x^2 - 5x + 4 - 5x^3 + 7x - 4

  3. Combine like terms: Identify terms with the same variables and exponents, and add their coefficients:

    (9x^3 - 5x^3) + 2x^2 + (-5x + 7x) + (4 - 4)

  4. Final result:

    4x^3 + 2x^2 + 2x

The Simplified Expression

Therefore, the simplified form of the polynomial expression (9x^3+2x^2-5x+4)-(5x^3-7x+4) is 4x^3 + 2x^2 + 2x.

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