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Chapter 10: Problem 24

In the following exercises, add or subtract the monomials. $$13 a-3 a$$

Short Answer

Expert verified
10a

Step by step solution

01

Identify the Monomials

The given expression contains two monomials: \(13a\) and \(-3a\).
02

Ensure Like Terms

Check that the monomials are like terms. Both \(13a\) and \(-3a\) have the variable 'a', so they are like terms and can be combined.
03

Add or Subtract the Coefficients

To combine the monomials, add or subtract their coefficients. Calculate \(13 - 3\).
04

Simplify

Perform the subtraction: \(13 - 3 = 10\). Therefore, the combined monomial is \(10a\).

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Key Concepts

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

Like Terms
When dealing with algebraic expressions, like terms are essential for simplification. Like terms are terms with the same variable part. For example, in the expression \(13a - 3a\), both terms involve the variable 'a'.
This means they can be combined through addition or subtraction. Like terms must not only have the same variable but also the same exponent on that variable. For example, \(5x\textsuperscript{2}\text{ and } 3x\textsuperscript{2}\) are like terms, but \(5x\textsuperscript{2}\text{ and } 3x\) are not.
Identifying like terms is the first step toward simplifying expressions. This concept helps make complex algebra much more manageable.
Adding Coefficients
To combine like terms, we need to focus on their coefficients. The coefficient is the numerical part of the term. For instance, in the term \(13a\), 13 is the coefficient.
Adding coefficients is straightforward. If the term was \(7b + 2b\), since both terms have 'b' as the variable, we add the coefficients: \(7 + 2 = 9\).
So, \(7b + 2b = 9b\). This simplified form is easier to work with, whether you're solving equations or performing further operations on the expression.
Always combine like terms by adding their coefficients while keeping the variable part unchanged.
Subtracting Coefficients
Just as we can add coefficients of like terms, we can also subtract them. Let's take the original exercise: \(13a - 3a\). Both terms are like terms because they have the same variable 'a'. The next step is to subtract the coefficients.
Subtracting the coefficients means solving \(13 - 3\), which equals 10.
Hence, \(13a - 3a = 10a\).
When subtracting coefficients, make sure you subtract the numerical part while keeping the variable unchanged.
This approach is useful for simplifying expressions and solving algebraic equations efficiently.

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Most popular questions from this chapter

Multiply using any method. $$(4 y-1)\left(6 y^{2}-12 y+5\right)$$

Multiply using any method. $$(5 b-2)\left(3 b^{2}+b-9\right)$$

Divide the monomials. $$\frac{-30 x^{8}}{-36 x^{9}}$$

Simplify each expression. $$\frac{x^{4}}{x^{-5}}$$

Simplify. $$r^{-5} \cdot r^{-4}$$
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