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Chapter 7: Problem 130

In the following exercises, simplify using the distributive property. $$-12-(u+10)$$

Short Answer

Expert verified
-22 - u

Step by step solution

01

- Identify terms inside the parentheses

The expression is -12-(u+10). Identify the terms inside the parentheses, which are u and 10.
02

- Apply the distributive property

Use the distributive property to distribute the negative sign -(u+10). Distributing the negative sign results in -u - 10.
03

- Simplify the expression

Combine all terms to get the simplified expression. The original expression now is -12 - u - 10. Combine the numeric constants to get -22 - u.

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Key Concepts

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

Simplifying Expressions
Simplifying an algebraic expression means to make it as concise as possible while still maintaining its value. To simplify an expression like \(-12-(u+10)\), you have to break it down step by step.
First, identify terms within parentheses and understand what operations need to be performed鈥攈ere we see \(u\) and 10 are inside the parentheses. Simplifying expressions often involves using the distributive property, combining like terms, and ensuring all parts of the expression are simplified properly.
This process not only makes handling the expression easier but also prepares it for further operations, if needed.
Combining Like Terms
Combining like terms is essential in simplifying your expressions. 'Like terms' are terms that contain the same variables raised to the same power. In our exercise, the terms we need to focus on are numerical constants and the variable term.
In the simplified form of our example \(-12-u-10\), you can see the constants -12 and -10 can be combined. Adding these together simplifies the number part of the expression, leading us to \(-22\). So, combining like terms gives you a neat, simpler expression: \(-22-u\).
This step is crucial because it reduces the expression to its most basic form, making further algebraic operations more straightforward and less prone to error.
Applying the Distributive Property
The distributive property helps to break down expressions within parentheses. For the exercise \(-12-(u+10)\), we need to distribute the negative sign across \(u+10\).
When you distribute, you multiply each term inside the parentheses by the factor outside the parentheses. Here, it means transforming \(-(u+10)\) to \(-u - 10\).
The distributive property is particularly useful when dealing with multi-term expressions. It allows you to expand and simplify expressions efficiently. Always apply the distributive property before combining like terms to ensure your calculations are accurate.

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