(-3a%5E3c%5E2)(-4a%5E2b%5E4c%5E3).jpeg "(-5abc^4)(-3a^3c^2)(-4a^2b^4c^3)")
Simplifying Polynomial Expressions: A Step-by-Step Guide
This article will guide you through the process of simplifying the polynomial expression (-5abc^4)(-3a^3c^2)(-4a^2b^4c^3).
Understanding the Basics
Before we begin, let's review a few key concepts:
- Coefficients: The numerical factors in a term (e.g., -5, -3, -4 in our expression).
- Variables: The letters representing unknown values (e.g., a, b, c in our expression).
- Exponents: The small numbers written above and to the right of variables, indicating how many times the variable is multiplied by itself (e.g., c^4 means c multiplied by itself 4 times).
Simplifying the Expression
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Multiply the coefficients: (-5) * (-3) * (-4) = -60
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Multiply the variables:
- a: a * a^3 * a^2 = a^(1+3+2) = a^6
- b: b * b^4 = b^(1+4) = b^5
- c: c^4 * c^2 * c^3 = c^(4+2+3) = c^9
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Combine the results: -60 * a^6 * b^5 * c^9 = -60a^6b^5c^9
Final Result
The simplified form of the expression (-5abc^4)(-3a^3c^2)(-4a^2b^4c^3) is -60a^6b^5c^9.
Key Takeaways
- To multiply monomials, multiply the coefficients and add the exponents of the same variables.
- Keep track of the signs of the coefficients to determine the final sign of the expression.
By following these steps, you can simplify complex polynomial expressions with confidence.