(4x^3-5x^2+7)+(2x^2+6x-11)

Jasonbradley

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Jun 16, 2024

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Simplifying Polynomial Expressions

This article will guide you through the process of simplifying the polynomial expression: (4x^3 - 5x^2 + 7) + (2x^2 + 6x - 11).

Understanding the Problem

We are given two polynomial expressions enclosed in parentheses. The "+" sign between the parentheses indicates that we need to add these two expressions together.

Simplifying the Expression

To simplify the expression, we can follow these steps:

1. Remove the parentheses: Since we are adding, the parentheses have no effect on the signs of the terms inside them. (4x^3 - 5x^2 + 7) + (2x^2 + 6x - 11) = 4x^3 - 5x^2 + 7 + 2x^2 + 6x - 11

2. Combine like terms: Identify terms with the same variable and exponent. Add their coefficients.

   • x^3 terms: 4x^3
   • x^2 terms: -5x^2 + 2x^2 = -3x^2
   • x terms: 6x
   • Constant terms: 7 - 11 = -4

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

   4x^3 - 3x^2 + 6x - 4

Final Answer

The simplified form of the expression (4x^3 - 5x^2 + 7) + (2x^2 + 6x - 11) is 4x^3 - 3x^2 + 6x - 4.