(8a^2-3a+4)-(-5a^2-2a-16)

Jasonbradley

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Jun 16, 2024

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Simplifying Polynomial Expressions: (8a^2-3a+4)-(-5a^2-2a-16)

This article will guide you through simplifying the polynomial expression: (8a^2-3a+4)-(-5a^2-2a-16).

Understanding the Basics

Before we begin, let's understand some fundamental concepts:

• Polynomial: An expression consisting of variables and coefficients, combined using addition, subtraction, and multiplication.
• Like Terms: Terms with the same variable and exponent. For example, 3a^2 and -5a^2 are like terms, while 3a^2 and 3a are not.
• Simplifying: Combining like terms to express the polynomial in its most compact form.

Step-by-Step Solution

1. Distribute the Negative Sign: The minus sign before the second parenthesis indicates we need to multiply each term inside by -1.

   (8a^2 - 3a + 4) + (5a^2 + 2a + 16)

2. Combine Like Terms: Group together terms with the same variable and exponent:

   (8a^2 + 5a^2) + (-3a + 2a) + (4 + 16)

3. Simplify: Combine the coefficients of each group of like terms:

   13a^2 - a + 20

Final Result

The simplified expression is 13a^2 - a + 20.