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Chapter 5: Problem 65

Add. $$ \begin{array}{r}{21 p-8} \\ {-9 p+4} \\ \hline\end{array} $$

Short Answer

Expert verified
12p - 4

Step by step solution

01

Write down the two algebraic expressions

Start by writing the two expressions on top of each other, aligning the like terms (terms with the same variable). $$ \begin{array}{r}{21p - 8} \ {-9p + 4} \ \ \hlineotag \ \ \end{array} $$
02

Add the coefficients of the like terms

Add the coefficients of the terms with the variable \(p\). $$21p + (-9p) = 12p$$
03

Add the constant terms

Now, add the constant terms (the numbers without variables). $$ -8 + 4 = -4 $$
04

Combine the results from Steps 2 and 3

Combine the results to form the final expression. $$12p - 4$$

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Key Concepts

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

Combining like terms
When dealing with algebra, one essential skill is combining like terms. Like terms are terms that have the same variable raised to the same power. For instance, in the expression \(21p - 8 \ and \ -9p + 4\), the terms with the variable \(p\) are 21p and -9p.

Combining like terms means adding or subtracting these coefficients. By aligning and adding them, it simplifies the equation. For example:
  • Add 21p and -9p to combine them: \(21p + (-9p) = 12p\).
This simplification helps in further calculations and a clearer understanding of the expression. Make sure to always carefully combine only like terms to maintain accuracy.
Algebraic addition
Algebraic addition involves the process of adding algebraic expressions together. These expressions typically include variables and constants. The critical point in algebraic addition is to ensure that you're only combining like terms. Let's reconsider the given problem:

\[\begin{array}{r} 21p - 8 \ -9p + 4 \ \hline \end{array}\]
When adding these expressions, start by separately focusing on the terms with variables and constants:
  • First, add the terms with \(p\): \(21p + (-9p) = 12p\)
  • Next, add the constants: \(-8 + 4 = -4\)
By breaking down the steps and adding like terms first, algebraic addition becomes a simpler and more manageable task.
Coefficients
Coefficients are the numerical parts of terms in algebraic expressions. For instance, in the term \(21p\), the number 21 is the coefficient, and \(p\) is the variable. Understanding coefficients is vital for combining like terms effectively. Let's break down the given problem while focusing on coefficients:

  • Identify coefficients of terms with \(p\): Here, we have coefficients 21 and -9 for the terms \(21p\) and \(-9p\).

  • Combine these coefficients: \(21 + (-9) = 12\). So, \(21p + (-9p) = 12p\).
Evaluating the right coefficients makes computations more straightforward and accurate. Remember, coefficients directly influence the final outcome of algebraic operations.

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