(7x^4y^2-2x^2y^2-5x^3y^4) (3x^2y)

Jasonbradley

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Jun 16, 2024

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Multiplying Polynomials: (7x⁴y² - 2x²y² - 5x³y⁴) (3x²y)

This article will guide you through the process of multiplying the polynomials (7x⁴y² - 2x²y² - 5x³y⁴) and (3x²y). We will use the distributive property to simplify this expression.

The Distributive Property

The distributive property states that for any numbers a, b, and c:

a(b + c) = ab + ac

We can apply this property to multiply polynomials by distributing each term of the first polynomial to each term of the second polynomial.

Applying the Distributive Property

1. Distribute the first term (3x²y) to each term inside the first polynomial:

   (3x²y) * (7x⁴y²) = 21x⁶y³ (3x²y) * (-2x²y²) = -6x⁴y³ (3x²y) * (-5x³y⁴) = -15x⁵y⁵

2. Combine the resulting terms:

   21x⁶y³ - 6x⁴y³ - 15x⁵y⁵

Simplified Expression

Therefore, the simplified expression for (7x⁴y² - 2x²y² - 5x³y⁴) (3x²y) is 21x⁶y³ - 6x⁴y³ - 15x⁵y⁵.