-(4ab%5E2-6ab%2B2a%2B3ab).jpeg "(12a^2b-8a+5a^2b-2ab)-(4ab^2-6ab+2a+3ab)")
Simplifying Algebraic Expressions: A Step-by-Step Guide
This article will guide you through the process of simplifying the algebraic expression: (12a^2b-8a+5a^2b-2ab)-(4ab^2-6ab+2a+3ab)
Understanding the Basics
Before we begin simplifying, let's understand the key concepts:
- Terms: An algebraic expression is made up of terms, which are separated by addition or subtraction signs. For example, in the expression 12a^2b - 8a, 12a^2b and -8a are individual terms.
- Coefficients: The numerical part of a term is called the coefficient. For instance, in the term 12a^2b, the coefficient is 12.
- Variables: The letters representing unknown quantities are called variables. In the term 5a^2b, a and b are variables.
- Like terms: Terms that have the same variables raised to the same powers are called like terms. For example, 12a^2b and 5a^2b are like terms.
Simplifying the Expression
-
Distribute the negative sign: The minus sign in front of the second set of parentheses means we need to multiply each term inside the parentheses by -1. This gives us: (12a^2b - 8a + 5a^2b - 2ab) + (-4ab^2 + 6ab - 2a - 3ab)
-
Combine like terms: Now, we'll group together the terms with the same variables and exponents: (12a^2b + 5a^2b) + (-8a - 2a) + (-2ab + 6ab - 3ab) - 4ab^2
-
Simplify: Perform the arithmetic operations on the coefficients of each group of like terms: 17a^2b - 10a + ab - 4ab^2
Final Simplified Expression
The simplified form of the given expression is 17a^2b - 10a + ab - 4ab^2. It is important to remember that the order of terms can vary, but the final result will be equivalent.