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(5x^2-3x+4)+(6x-3x^2-3)

2 min read Jun 16, 2024
(5x^2-3x+4)+(6x-3x^2-3)

Simplifying Polynomial Expressions: (5x^2-3x+4)+(6x-3x^2-3)

This article will guide you through simplifying the polynomial expression: (5x^2-3x+4)+(6x-3x^2-3).

Understanding the Basics

Before we begin, let's quickly review some essential concepts:

  • Polynomials: Expressions consisting of variables and constants combined using addition, subtraction, and multiplication, with non-negative integer exponents.
  • Like terms: Terms that have the same variable and exponent. For example, 5x^2 and -3x^2 are like terms.
  • Combining like terms: When adding or subtracting polynomials, we combine like terms by adding or subtracting their coefficients.

Simplifying the Expression

  1. Identify Like Terms: In the given expression, we can group the like terms together:

    (5x^2 - 3x^2) + (-3x + 6x) + (4 - 3)

  2. Combine Like Terms: Now, we simply combine the coefficients of the like terms:

    2x^2 + 3x + 1

Final Result

Therefore, the simplified form of the polynomial expression (5x^2-3x+4)+(6x-3x^2-3) is 2x^2 + 3x + 1.

Key Points

  • Always remember to group like terms before combining them.
  • Pay attention to the signs (positive or negative) of the coefficients.
  • Combining like terms is a fundamental skill in algebra, making it easier to manipulate and solve equations.

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