(2a+5b)(3a^2-4ab-2b^2)

Jasonbradley

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Jun 16, 2024

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Expanding the Expression (2a + 5b)(3a² - 4ab - 2b²)

This article will guide you through expanding the given algebraic expression using the distributive property.

Understanding the Distributive Property

The distributive property states that multiplying a sum by a number is the same as multiplying each addend in the sum by the number and then adding the products.

Mathematically, this can be represented as: a(b + c) = ab + ac

Expanding the Expression

1. Identify the terms: We have two terms in the first set of parentheses: 2a and 5b.
2. Distribute: We need to multiply each term in the first set of parentheses by each term in the second set of parentheses. This means we will have a total of 6 multiplications.
3. Multiply:
   • 2a * 3a² = 6a³
   • 2a * -4ab = -8a²b
   • 2a * -2b² = -4ab²
   • 5b * 3a² = 15a²b
   • 5b * -4ab = -20ab²
   • 5b * -2b² = -10b³
4. Combine like terms: Notice that some of the terms have the same variables and exponents. These are called like terms. We can combine them to simplify the expression.
   • 6a³
   • -8a²b + 15a²b = 7a²b
   • -4ab² - 20ab² = -24ab²
   • -10b³

Final Result

Therefore, the expanded form of the expression (2a + 5b)(3a² - 4ab - 2b²) is:

(2a + 5b)(3a² - 4ab - 2b²) = 6a³ + 7a²b - 24ab² - 10b³