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Chapter 1: Problem 63

Simplify each expression. \(6 y^{2}+11 y^{2}-8 y^{2}\)

Short Answer

Expert verified
The simplified expression is \ 9y^{2} \.

Step by step solution

01

Combine Like Terms

First, identify like terms in the expression. Here, all terms are like terms because they all have the same variable part, which is \(y^{2}\).
02

Add and Subtract Coefficients

Add and subtract the coefficients of the like terms: \(6 + 11 - 8\). This gives \(9\).
03

Write the Simplified Expression

Attach the simplified coefficient to the common variable part \(y^{2}\). The simplified expression is \ 9y^{2} \.

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Key Concepts

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

What are Like Terms?
In algebra, like terms are terms that have the same variable part with the same exponent. This means they can be combined through addition or subtraction. In the expression we are working with,
  • 6y虏, 11y虏, and -8y虏
The variable part for all three terms is y虏, hence they are like terms. By identifying like terms, you only need to focus on their coefficients when simplifying. Remember, like terms must have exactly the same variables raised to the same powers. Numbers without variables are also considered like terms.
Understanding Coefficients
Coefficients are the numerical parts of terms in an algebraic expression. In the expression 6y虏, 11y虏, and -8y虏:
  • 6 is the coefficient of y虏 in the first term.
  • 11 is the coefficient of y虏 in the second term.
  • -8 is the coefficient of y虏 in the third term.
When simplifying expressions involving like terms, you'll be adding or subtracting these coefficients. For our example, we combined the coefficients 6, 11, and -8 to get 9. The variable part (y虏) remains the same.
Creating a Simplified Expression
A simplified expression is one where all like terms have been combined, and there are no parentheses left. In our example, we started with 6y虏 + 11y虏 - 8y虏.
  • First, we identified our like terms.
  • Then, we added their coefficients together: 6 + 11 - 8.
This gave us a new coefficient of 9. Finally, we attached this new coefficient to the variable part y虏. So, the simplified expression is 9y虏. Simplifying expressions makes them easier to work with, especially in more complex algebraic operations.

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