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(3a+4b)-(5a-2b)

2 min read Jun 16, 2024
(3a+4b)-(5a-2b)

Simplifying Algebraic Expressions: (3a + 4b) - (5a - 2b)

This article will guide you through the process of simplifying the algebraic expression (3a + 4b) - (5a - 2b).

Understanding the Basics

Before we begin simplifying, let's understand the key concepts involved:

  • Variables: In algebra, variables represent unknown values. In this expression, a and b are variables.
  • Coefficients: Numbers that are multiplied by variables are called coefficients. For example, in the term 3a, 3 is the coefficient.
  • Terms: A term is a combination of a coefficient and a variable, or just a number. For example, 3a, 4b, 5a, and 2b are all terms.

Simplifying the Expression

  1. Distribute the negative sign: The minus sign in front of the second set of parentheses means we multiply each term inside the parentheses by -1: (3a + 4b) + (-1 * 5a) + (-1 * -2b)

  2. Simplify: 3a + 4b - 5a + 2b

  3. Combine like terms: Like terms have the same variables raised to the same power. Group the a terms and the b terms: (3a - 5a) + (4b + 2b)

  4. Simplify further: -2a + 6b

Final Result

Therefore, the simplified form of (3a + 4b) - (5a - 2b) is -2a + 6b.

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