Simplifying Algebraic Expressions: (7a^2 + 5a + 3) + (3a^2 + 2a  4)
This article explores the process of simplifying the algebraic expression (7a^2 + 5a + 3) + (3a^2 + 2a  4).
Understanding the Problem
The expression involves combining two sets of terms. Each set contains variables (represented by 'a') raised to different powers, along with constant terms. To simplify the expression, we need to combine like terms.
Combining Like Terms
Like terms are those that have the same variable raised to the same power.

Step 1: Identify like terms:
 a^2 terms: 7a^2 and 3a^2
 a terms: 5a and 2a
 Constant terms: 3 and 4

Step 2: Combine like terms by adding their coefficients:
 7a^2  3a^2 = 4a^2
 5a + 2a = 7a
 3  4 = 1
The Simplified Expression
After combining like terms, the simplified expression is: 4a^2 + 7a  1
Conclusion
By following the steps of identifying and combining like terms, we have simplified the algebraic expression (7a^2 + 5a + 3) + (3a^2 + 2a  4) into its simplest form, which is 4a^2 + 7a  1.