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Chapter 1: Problem 8

Simplify: \(3 y+8 y\).

Short Answer

Expert verified
The simplified form is \(11y\).

Step by step solution

01

Identify Like Terms

The expression given is \(3y + 8y\). We need to find the like terms. In this case, both terms have 'y' as a variable, making them like terms. This means we can add them together.
02

Add the Coefficients

For like terms, you add their coefficients. The coefficient of the first term is 3 and the coefficient of the second term is 8. Add them together: \(3 + 8 = 11\).
03

Write the Simplified Expression

Since we added the coefficients of the like terms, we keep the variable part 'y' attached to the sum. Therefore, the simplified expression is \(11y\).

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Key Concepts

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

Like Terms
When working with algebraic expressions, you'll often encounter terms that can be combined. These are known as like terms. Understanding what makes terms "like" is key to simplifying expressions effectively.
Like terms are terms that have identical variable parts. Even though the coefficients (the numerical part) might be different, the variable and its exponent (if present) must be the same.
  • Consider the terms: \(3y\) and \(8y\). Both contain the variable \(y\), hence they are like terms.
  • On the other hand, \(2x\) and \(3y\) are not like terms because their variables \(x\) and \(y\) are different.
By recognizing like terms, you can combine them, streamlining the process of working with algebraic expressions.
Coefficients
In algebraic terms, coefficients play a crucial role. They are the numerical factor that multiplies the variable in each term.
Understanding coefficients is essential for combining like terms. In the expression \(3y + 8y\), the coefficients are \(3\) and \(8\). These numbers denote how many times the variable \(y\) is being multiplied.
  • The process of adding like terms involves summing the coefficients of those terms.
  • So, for \(3y + 8y\), you add the coefficients: \(3 + 8\).
  • This results in the simplified coefficient: \(11\).
Knowing how to manipulate coefficients allows you to effectively simplify expressions.
Algebraic Expressions
Algebraic expressions are a fundamental part of algebra. They consist of numbers, variables, and operations (like addition or subtraction) arranged together. These expressions represent generalized numbers and can be manipulated in various ways.
When you simplify algebraic expressions, you're looking to make them as concise as possible without changing their value.
  • For example, the expression \(3y + 8y\) is initially given as two separate terms.
  • After recognizing they are like terms, you combine them by adding their coefficients.
  • This gives you the simplified expression: \(11y\).
The simplicity allows easier interpretation and further use of the expression in more complex equations or functions.

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