(2x^3+7x^2+x)+(2x^2-4x-12)

Jasonbradley

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Jun 16, 2024

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Simplifying Polynomial Expressions

This article will guide you through simplifying the following polynomial expression:

(2x³ + 7x² + x) + (2x² - 4x - 12)

Understanding Polynomials

Polynomials are algebraic expressions consisting of variables and constants, combined using addition, subtraction, and multiplication, where exponents of variables are non-negative integers.

Simplifying the Expression

1. Identify Like Terms:

   • Like terms have the same variables raised to the same powers.
   • In our expression, we have:
     • x³ terms: 2x³
     • x² terms: 7x² and 2x²
     • x terms: x and -4x
     • Constant terms: -12

2. Combine Like Terms:

   • Add the coefficients of the like terms.
   • (2x³ + 7x² + x) + (2x² - 4x - 12) = 2x³ + (7x² + 2x²) + (x - 4x) - 12

3. Simplify:

   • Combine the coefficients: 2x³ + 9x² - 3x - 12

Final Result

The simplified form of the expression (2x³ + 7x² + x) + (2x² - 4x - 12) is 2x³ + 9x² - 3x - 12.