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Chapter 1: Problem 330

In the following exercises, simplify. $$ 27 c+16-27 c $$

Short Answer

Expert verified
The simplified expression is \(16\).

Step by step solution

01

Identify Like Terms

The expression given is \(27c + 16 - 27c\). Notice that \(27c\) and \(-27c\) are like terms because they both include the variable \(c\).
02

Combine Like Terms

Now, combine the like terms by adding them: \(27c - 27c\). These cancel each other out because \(27c - 27c = 0\). Therefore, the expression simplifies to \(0 + 16\).
03

Simplify the Constant Term

Lastly, add the constant term: \(0 + 16 = 16\). Therefore, the simplified expression is \(16\).

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Key Concepts

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

like terms
Like terms in algebra are terms that have the same variable raised to the same power. For example, in the expression given, \(27c + 16 - 27c\), the terms \(27c\) and \(-27c\) are like terms because they both involve the variable \(c\). It doesn't matter that one term is positive and the other is negative. As long as the variable part is the same, they are considered like terms. Recognizing like terms is the first step in simplifying algebraic expressions.
combining like terms
When simplifying expressions, combining like terms is essential. In the exercise, we first identified the like terms, \(27c\) and \(-27c\). To combine them, we perform math operations on their coefficients. For this example, it looks like this: \(27c - 27c\). Adding these two terms results in zero, as any number minus itself equals zero. Thus, \(27c - 27c = 0\). By combining like terms, we simplify the expression to a new form that is easier to understand and work with.
constant term
A constant term is a term in an algebraic expression that does not contain any variables. In the given exercise, the term \(16\) is a constant term. Constants remain unchanged while simplifying an expression because they don't have variables associated with them. After combining like terms and simplifying, you'll add or subtract the constant term to find the final simplified expression. For instance, once we combined the like terms and got \(0\), we added the constant term \(16\) to it. So, \(0 + 16 = 16\). Understanding constants helps make sure the expressions stay accurate through the simplification process.

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