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Simplifying Polynomial Expressions: A Step-by-Step Guide
This article will guide you through the process of simplifying the following polynomial expression:
(−3p³ + 5p² − 2p) + (−p³ − 8p² − 15p)
Understanding the Basics:
- Polynomial: A polynomial is an expression consisting of variables and coefficients, combined using addition, subtraction, and multiplication. The exponents of the variables must be non-negative integers.
- Like Terms: Terms with the same variable and the same exponent are considered like terms. For example, 3p² and -8p² are like terms, while 5p² and 2p are not.
Simplifying the Expression:
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Identify Like Terms:
- p³ terms: -3p³ and -p³
- p² terms: 5p² and -8p²
- p terms: -2p and -15p
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Combine Like Terms:
- p³ terms: -3p³ + (-p³) = -4p³
- p² terms: 5p² + (-8p²) = -3p²
- p terms: -2p + (-15p) = -17p
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Combine the Simplified Terms: -4p³ - 3p² - 17p
Therefore, the simplified form of the polynomial expression (−3p³ + 5p² − 2p) + (−p³ − 8p² − 15p) is -4p³ - 3p² - 17p.
Key Points to Remember:
- Order of Operations: Always follow the order of operations (PEMDAS/BODMAS) when simplifying expressions.
- Sign Conventions: Pay close attention to the signs of the terms when combining them.
- Like Terms Only: Combine only like terms.
By following these steps, you can confidently simplify any polynomial expression. Remember to practice, and soon you'll become a pro at combining like terms!