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

Jasonbradley

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Jun 16, 2024

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Expanding the Expression (2x + 5y)(3x² - 4xy + 2y²)

This article will explore how to expand the given expression (2x + 5y)(3x² - 4xy + 2y²). We will use the distributive property to multiply each term in the first expression by each term in the second expression.

The Distributive Property

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

• a(b + c) = ab + ac

Expanding the Expression

Let's apply the distributive property to our expression:

1. Multiply 2x by each term in the second expression:

   • 2x * 3x² = 6x³
   • 2x * (-4xy) = -8x²y
   • 2x * 2y² = 4xy²

2. Multiply 5y by each term in the second expression:

   • 5y * 3x² = 15x²y
   • 5y * (-4xy) = -20xy²
   • 5y * 2y² = 10y³

3. Add all the resulting terms together:

   • 6x³ - 8x²y + 4xy² + 15x²y - 20xy² + 10y³

4. Combine like terms:

   • 6x³ + 7x²y - 16xy² + 10y³

Final Result

Therefore, the expanded form of the expression (2x + 5y)(3x² - 4xy + 2y²) is 6x³ + 7x²y - 16xy² + 10y³.