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Chapter 3: Problem 65

Combine the like terms. $$4 a^{2} b-6 a^{2} b$$

Short Answer

Expert verified
-2 a^{2} b

Step by step solution

01

Identify the Like Terms

Notice that the terms have the same variables with identical exponents: oo
02

Combine the Coefficients

Combine the coefficients of the given terms. oo 4 a^{2} b-6 a^{2} b
03

Simplify the Expression

Add the coefficients together:oo(4 a^{2} b-6 a^{2} b)oo
04

Final Answer

Combine the coefficients and write the final expression with the common terms: oo-2 a^{2} b -6 a^{2} b

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Like Terms
In algebra, it is vital to understand the concept of _like terms_. Like terms are terms that have the same variables raised to the same power. For instance, in the expression \(4a^{2}b - 6a^{2}b\), both terms are considered like terms because they both contain \(a^{2}b\). The coefficients of these terms can differ, but as long as the variable part is identical, they are like terms. When you combine like terms, you simply add or subtract their coefficients.
Coefficients
_Coefficients_ are the numerical part of terms that are multiplied by the variables. For example, in the term \(4a^{2}b\), the coefficient is 4. Similarly, in \(-6a^{2}b\), the coefficient is -6. When simplifying expressions with like terms, identify the coefficients and then perform the required arithmetic operation. For the expression \(4a^{2}b - 6a^{2}b\), you combine the coefficients 4 and -6 by subtracting 6 from 4, which results in -2.
Polynomials
A _polynomial_ is an expression made up of terms that include variables, coefficients, and exponents. Each term in a polynomial can have constants and variables multiplied together, but the exponents must be whole numbers. Our example expression, \(4a^{2}b - 6a^{2}b\), is a polynomial because it consists of multiple terms. Simplifying this polynomial involves combining like terms into one single term, making it easier to handle in further calculations.
Algebra
_Algebra_ is a branch of mathematics dealing with symbols and the rules for manipulating those symbols. These symbols, often represented by letters like \(a\) and \(b\), stand in for numbers and allow us to formulate equations and expressions. The exercise provided involves basic algebraic manipulation, which includes identifying like terms, working with coefficients, and simplifying polynomials. Mastery of these fundamental concepts is essential for solving more complex algebraic problems.

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