(7x^3+15x^2-12x)+(x^3-4x^2-15x+1)

Jasonbradley

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Jun 16, 2024

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Simplifying Polynomial Expressions

This article will explore the process of simplifying the polynomial expression: (7x^3 + 15x^2 - 12x) + (x^3 - 4x^2 - 15x + 1).

Understanding Polynomials

A polynomial is a mathematical expression consisting of variables and coefficients, combined using addition, subtraction, and multiplication. Each term in a polynomial has a specific degree, which is the power of the variable in that term.

Simplifying the Expression

To simplify the given expression, we need to combine like terms. Like terms have the same variable and the same exponent.

1. Identify like terms:

   • x^3 terms: 7x^3 + x^3
   • x^2 terms: 15x^2 - 4x^2
   • x terms: -12x - 15x
   • Constant terms: +1

2. Combine like terms:

   • (7x^3 + x^3) + (15x^2 - 4x^2) + (-12x - 15x) + 1

3. Simplify:

   • 8x^3 + 11x^2 - 27x + 1

Result

The simplified form of the expression (7x^3 + 15x^2 - 12x) + (x^3 - 4x^2 - 15x + 1) is 8x^3 + 11x^2 - 27x + 1.