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Chapter 1: Problem 64

Simplify by combining like terms. See Example 5 . $$12 y-17 y$$

Short Answer

Expert verified
The simplified expression is \(-5y\).

Step by step solution

01

Identify Like Terms

The expression is given as \(12y - 17y\). Here, the terms are \(12y\) and \(-17y\), which are like terms because they both contain the variable \(y\) and can be combined.
02

Combine Like Terms

To combine \(12y\) and \(-17y\), keep the variable \(y\) and perform the subtraction: \(12 - 17 = -5\). Thus, the combined expression is \(-5y\).

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Key Concepts

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

Combining Like Terms
When you hear the term "combining like terms," think of organizing and simplifying an expression by putting similar items together. A "like term" is simply a term that has the same variables raised to the same power. For example, in the expression \(12y - 17y\), both terms are like terms because they contain the variable \(y\) to the same power of 1.

Here's a simple way to look at it:
  • Identify like terms: Same variables, same exponents.
  • Combine them by calculating the coefficients (numbers in front of the variables).
In summary, when combining like terms, you are basically performing addition or subtraction on their coefficients, while keeping the variable part unchanged. This helps to reduce the expression to its simplest form.
Algebraic Expressions
An algebraic expression is a mathematical phrase that can include numbers, variables, and operations. Variables are symbols (like \(x\) or \(y\)) that represent unknown values and can vary. These expressions are foundational in algebra since they form the building blocks for more complex problem-solving.

In the expression \(12y - 17y\), "12" and "-17" are coefficients that are multiplied by the variable \(y\). Expressions can become simpler or more manageable when we correctly combine like terms, which is a critical step in solving equations or inequalities.

Remember:
  • An algebraic expression doesn鈥檛 include an equality sign鈥攊t鈥檚 not an equation until it does.
  • Knowing how to identify terms in an expression is key to any simplification.
Understanding and manipulating these expressions are essential skills for progressing in algebraic problem-solving.
Intermediate Algebra
Intermediate algebra focuses on building and refining skills learned in basic algebra. It includes working with more complicated expressions and performing operations that prepare students for topics in calculus and beyond.

When dealing with tasks like combining like terms in Expressions such as \(12y - 17y\), you are honing your ability to simplify expressions, which is critical in intermediate algebra.

Some key concepts in intermediate algebra include:
  • Solving equations and inequalities.
  • Understanding and applying functions.
  • Simplifying complex algebraic fractions and expressions.
These skills are crucial for tackling more advanced mathematical ideas and will serve you well as you delve deeper into the world of mathematics.

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