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Chapter 6: Problem 13

Add or subtract the monomials. $$4 a-9 a$$

Short Answer

Expert verified
-5a

Step by step solution

01

Combine Like Terms

Both terms, 4a and -9a, are like terms because they both have the variable 'a'. Now, combine them by adding their coefficients.
02

Add the Coefficients

Add the coefficients: 4 + (-9) which simplifies to -5.
03

Write the Result

The combined term is -5a.

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Key Concepts

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

Monomials
Monomials are algebraic expressions that contain just one term. A term is a combination of numbers and variables raised to a power. For example, in the exercise above, both \(4a\) and \(-9a\) are monomials. They each have a single variable \(a\).
Monomials can be:
  • A number (like 5).
  • A variable (like x).
  • A product of a number and one or more variables (like 4a or -9a).
Monomials make it easier to perform algebraic operations like addition or subtraction.
Coefficients
Coefficients are the numerical part of monomials. In the exercise \(4a - 9a\), the coefficients are \(4\) and \(-9\).
Coefficients help in indicating how many times a variable is counted. For example, in \(4a\), the coefficient 4 means we have four 'a's. Similarly, \(-9a\) means we have negative nine 'a's.
When combining like terms, we add or subtract their coefficients. In this exercise: \(4a - 9a = -5a\). By adding the coefficients \(4 + (-9)\), we get \(-5\), which is the coefficient of the resulting term.
Simplifying Algebraic Expressions
Simplifying algebraic expressions involves combining like terms to make the expression shorter and easier to understand.
Like terms are terms that have identical variables raised to the same power. In \(4a - 9a\), both terms are like terms because they contain the variable \(a\).
To simplify, we combine these terms by adding or subtracting their coefficients: \(4a - 9a\) simplifies to \(-5a\).
Simplifying helps in solving equations and understanding mathematical relationships more efficiently.

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