Expanding the Expression (a + 2b)(3a + 2c)
This article will guide you through the process of expanding the expression (a + 2b)(3a + 2c).
Understanding the Concept
The expression (a + 2b)(3a + 2c) represents the multiplication of two binomials. To expand it, we need to distribute each term in the first binomial to each term in the second binomial. This process is often referred to as FOIL, standing for First, Outer, Inner, Last.
Applying FOIL Method

First: Multiply the first terms of each binomial:
 a * 3a = 3a²

Outer: Multiply the outer terms of the binomials:
 a * 2c = 2ac

Inner: Multiply the inner terms of the binomials:
 2b * 3a = 6ab

Last: Multiply the last terms of each binomial:
 2b * 2c = 4bc
Combining the Terms
Now, combine all the terms we obtained:
 3a² + 2ac + 6ab + 4bc
Final Expanded Form
Therefore, the expanded form of (a + 2b)(3a + 2c) is 3a² + 2ac + 6ab + 4bc.
Note
The order of the terms in the expanded form doesn't matter. You can rearrange them as long as you keep the signs correct.