(2x-3)+(2x-5x^2+13)-(x^2-1)

Jasonbradley

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Jun 16, 2024

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Simplifying Algebraic Expressions

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

(2x - 3) + (2x - 5x^2 + 13) - (x^2 - 1)

Understanding the Process

The key to simplifying this expression lies in combining like terms. This means grouping terms with the same variables and exponents together. To do so, we need to follow these steps:

1. Remove the parentheses: Since we are adding and subtracting the expressions inside the parentheses, we can remove them without changing the signs of the terms.
2. Identify like terms: Look for terms with the same variable and exponent. For example, '2x' and '2x' are like terms, while '2x' and '-5x^2' are not.
3. Combine like terms: Add or subtract the coefficients of the like terms.

Step-by-Step Solution

Let's simplify the expression step by step:

1. Remove parentheses: (2x - 3) + (2x - 5x^2 + 13) - (x^2 - 1) = 2x - 3 + 2x - 5x^2 + 13 - x^2 + 1

2. Identify like terms:

   • x^2 terms: -5x^2 and -x^2
   • x terms: 2x and 2x
   • Constant terms: -3, 13, and 1

3. Combine like terms:

   • -5x^2 - x^2 = -6x^2
   • 2x + 2x = 4x
   • -3 + 13 + 1 = 11

Simplified Expression

Therefore, the simplified expression is:

-6x^2 + 4x + 11