(2x^5y^2)(4xy^3)+(x^4y^4)(3x^2y)

Jasonbradley

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Jun 16, 2024

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Simplifying Polynomial Expressions

This article will explore how to simplify the polynomial expression: (2x⁵y²)(4xy³)+(x⁴y⁴)(3x²y).

Understanding the Basics

Before we dive into the simplification, let's review some fundamental concepts of polynomial expressions:

• Polynomials: Expressions containing variables and coefficients combined with addition, subtraction, and multiplication operations.
• Terms: Individual parts of a polynomial separated by addition or subtraction.
• Coefficients: Numerical factors multiplying variables.
• Variables: Symbols representing unknown values.
• Exponents: Small numbers written above and to the right of a variable, indicating the number of times the variable is multiplied by itself.

Simplifying the Expression

1. Apply the distributive property: This property states that multiplying a sum by a factor is the same as multiplying each term of the sum by that factor.

   (2x⁵y²)(4xy³)+(x⁴y⁴)(3x²y) = (24)(x⁵x)(y²y³) + (13)(x⁴x²)(y⁴y)

2. Combine like terms: This means multiplying coefficients and adding exponents of the same variable.

   8x⁶y⁵ + 3x⁶y⁵

3. Add the coefficients of like terms:

   11x⁶y⁵

Conclusion

The simplified form of the polynomial expression (2x⁵y²)(4xy³)+(x⁴y⁴)(3x²y) is 11x⁶y⁵. This process highlights the power of applying fundamental algebraic principles for simplifying complex expressions.