(4a+2)(6a^2-a+2)

Jasonbradley

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Jun 16, 2024

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Expanding the Expression (4a+2)(6a^2-a+2)

This article explores the process of expanding the expression (4a+2)(6a^2-a+2) using the distributive property.

The Distributive Property

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

a(b + c) = ab + ac

Expanding the Expression

To expand the expression (4a+2)(6a^2-a+2), we can apply the distributive property twice:

1. Distribute (4a + 2) over the terms in the second factor: (4a + 2)(6a^2 - a + 2) = 4a(6a^2 - a + 2) + 2(6a^2 - a + 2)

2. Distribute 4a and 2 over the terms in the parentheses: = (4a * 6a^2) + (4a * -a) + (4a * 2) + (2 * 6a^2) + (2 * -a) + (2 * 2)

3. Simplify by performing the multiplication: = 24a^3 - 4a^2 + 8a + 12a^2 - 2a + 4

4. Combine like terms: = 24a^3 + 8a^2 + 6a + 4

Therefore, the expanded form of (4a+2)(6a^2-a+2) is 24a^3 + 8a^2 + 6a + 4.