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

Distribute the first term (3x²y) to each term inside the first polynomial:
(3x²y) * (7x⁴y²) = 21x⁶y³ (3x²y) * (2x²y²) = 6x⁴y³ (3x²y) * (5x³y⁴) = 15x⁵y⁵

Combine the resulting terms:
21x⁶y³  6x⁴y³  15x⁵y⁵
Simplified Expression
Therefore, the simplified expression for (7x⁴y²  2x²y²  5x³y⁴) (3x²y) is 21x⁶y³  6x⁴y³  15x⁵y⁵.