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(2x4+x3−4x2+3)+(4x4−2x3−x2+10x+2)

2 min read Jun 16, 2024
(2x4+x3−4x2+3)+(4x4−2x3−x2+10x+2)

Simplifying Polynomial Expressions

In mathematics, polynomials are expressions consisting of variables and coefficients, combined using addition, subtraction, and multiplication. Simplifying polynomials involves combining like terms to reduce the expression to its simplest form.

Let's take a look at the following polynomial expression:

(2x⁴ + x³ - 4x² + 3) + (4x⁴ - 2x³ - x² + 10x + 2)

To simplify this expression, we need to follow these steps:

  1. Identify like terms: Look for terms with the same variable and exponent. In our example, these are:

    • x⁴: 2x⁴ and 4x⁴
    • x³: x³ and -2x³
    • x²: -4x² and -x²
    • x: 10x (This term is only present in the second set of parentheses)
    • Constant terms: 3 and 2

  2. Combine like terms: Add or subtract the coefficients of the like terms.

    • x⁴: 2x⁴ + 4x⁴ = 6x⁴
    • x³: x³ - 2x³ = -x³
    • x²: -4x² - x² = -5x²
    • x: 10x
    • Constant terms: 3 + 2 = 5

  3. Write the simplified expression: Combine the simplified terms:

    6x⁴ - x³ - 5x² + 10x + 5

Therefore, the simplified form of the given polynomial expression is 6x⁴ - x³ - 5x² + 10x + 5.

This process of combining like terms is fundamental to simplifying and manipulating polynomial expressions in various mathematical contexts.

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