Simplifying Algebraic Expressions: (a + 2b + 3c)  (4a + 6b  5c)
This article explores the simplification of the algebraic expression (a + 2b + 3c)  (4a + 6b  5c).
Understanding the Expression
The expression involves combining like terms, which are terms with the same variable raised to the same power. We can simplify this by distributing the negative sign in front of the second set of parentheses and then combining like terms.
Steps to Simplify

Distribute the negative sign: (a + 2b + 3c)  (4a + 6b  5c) = a + 2b + 3c  4a  6b + 5c

Combine like terms:
 a terms: a  4a = 3a
 b terms: 2b  6b = 4b
 c terms: 3c + 5c = 8c

Write the simplified expression: 3a  4b + 8c
Conclusion
Therefore, the simplified equivalent expression for (a + 2b + 3c)  (4a + 6b  5c) is 3a  4b + 8c.