%C3%976xy%5E3.jpeg "(3x^3y-1/2x^2+1/5xy)×6xy^3")
Multiplying Polynomials: (3x³y - 1/2x² + 1/5xy) × 6xy³
This article will guide you through the process of multiplying the polynomial (3x³y - 1/2x² + 1/5xy) by 6xy³.
Understanding the Process
The key to multiplying polynomials is to distribute each term in the first polynomial to every term in the second polynomial. This is similar to the distributive property of multiplication.
Step-by-Step Solution
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Distribute 6xy³ to each term in the first polynomial:
(3x³y - 1/2x² + 1/5xy) × 6xy³ = (3x³y × 6xy³) + (-1/2x² × 6xy³) + (1/5xy × 6xy³)
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Multiply the coefficients and add the exponents of like terms:
- (3x³y × 6xy³) = 18x⁴y⁴
- (-1/2x² × 6xy³) = -3x³y³
- (1/5xy × 6xy³) = 6/5x²y⁴
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Combine the results:
18x⁴y⁴ - 3x³y³ + 6/5x²y⁴
Final Answer
Therefore, the product of (3x³y - 1/2x² + 1/5xy) and 6xy³ is 18x⁴y⁴ - 3x³y³ + 6/5x²y⁴.
Key Takeaways
- Remember to distribute each term in the first polynomial to every term in the second polynomial.
- When multiplying terms, multiply the coefficients and add the exponents of like variables.
- Simplify the expression by combining like terms.
By following these steps, you can confidently multiply polynomials and arrive at the correct answer.