-%E2%80%93-(%E2%80%937x2y3-%2B-6xy2-%E2%80%93-2y)-place-the-correct-coefficients-in-the-difference.jpeg "(4x2y3 + 2xy2 – 2y) – (–7x2y3 + 6xy2 – 2y) Place The Correct Coefficients In The Difference")
Finding the Difference of Polynomials
This article will guide you through the process of finding the difference between two polynomials: (4x²y³ + 2xy² – 2y) – (–7x²y³ + 6xy² – 2y)
Understanding the Basics
- Polynomials: Expressions consisting of variables and constants combined using addition, subtraction, and multiplication.
- Coefficients: Numbers that multiply variables in a polynomial.
- Like Terms: Terms with the same variables raised to the same powers.
Step-by-Step Solution
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Distribute the Negative Sign:
- The minus sign in front of the second set of parentheses indicates subtraction.
- We distribute this negative sign to each term within the second set of parentheses:
(4x²y³ + 2xy² – 2y) + (7x²y³ - 6xy² + 2y)
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Combine Like Terms:
- Identify terms with the same variables and powers.
- Combine their coefficients:
(4x²y³ + 7x²y³) + (2xy² - 6xy²) + (-2y + 2y)
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Simplify:
- Add or subtract the coefficients of each set of like terms:
11x²y³ - 4xy² + 0
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Final Result:
- The difference between the two polynomials is:
11x²y³ - 4xy²
Summary
By distributing the negative sign, combining like terms, and simplifying, we have successfully found the difference between the two given polynomials. The resulting expression is 11x²y³ - 4xy².