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Subtracting Polynomials: A Step-by-Step Guide
This article will guide you through the process of subtracting the polynomial (6/5)x² - (4/5)x³ + (5/6) + (3/2)x from the polynomial (1/3)x³ - (5/2)x² + (3/5)x + (1/4).
Understanding the Process
Subtracting polynomials involves combining like terms after distributing the negative sign to all terms within the second polynomial. Let's break down the steps:
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Rewrite the expression:
- Begin by writing the expression as: (1/3)x³ - (5/2)x² + (3/5)x + (1/4) - [(6/5)x² - (4/5)x³ + (5/6) + (3/2)x]
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Distribute the negative sign:
- Multiply each term inside the brackets by -1. (1/3)x³ - (5/2)x² + (3/5)x + (1/4) - (6/5)x² + (4/5)x³ - (5/6) - (3/2)x
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Combine like terms:
- Group together terms with the same variable and exponent. [(1/3)x³ + (4/5)x³] + [-(5/2)x² - (6/5)x²] + [(3/5)x - (3/2)x] + [(1/4) - (5/6)]
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Simplify each group:
- Find a common denominator for each group of like terms and perform the addition or subtraction. [(5/15)x³ + (12/15)x³] + [-(25/10)x² - (12/10)x²] + [(6/10)x - (15/10)x] + [(3/12) - (10/12)]
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Final Result:
- Combine the simplified terms to get the final result. (17/15)x³ - (37/10)x² - (9/10)x - (7/12)
Conclusion
Subtracting polynomials involves careful attention to signs and combining like terms. By following the steps outlined above, you can confidently subtract any two polynomials.