Problem 49 Rewrite each expression using th... [FREE SOLUTION]

Chapter 1: Problem 49

Rewrite each expression using the distributive property. Simplify if possible. $$-2(5+7)$$

Short Answer

Expert verified

The expression $-2(5+7)$ using the distributive property can be rewritten as $-2 \cdot 5 + (-2) \cdot 7$, which simplifies to $-10 + (-14) = -24$. The final answer is $-24$.

Step by step solution

Identify the terms

First, identify the terms in the given expression, $-2(5+7)$. We have $a = -2$, $b = 5$, and $c = 7$.

Apply the distributive property

Now, apply the distributive property to the given expression by replacing the expression of the form $a(b+c)$ with $ab + ac$, as follows: $-2(5+7) = -2 \cdot 5 + (-2) \cdot 7$

Simplify the expression

Next, perform the multiplication in the rewritten expression: $-2 \cdot 5 + (-2) \cdot 7 = -10 + (-14)$ Now, simply add the two terms: $-10 + (-14) = -24$

Write the final answer

The simplified expression using the distributive property is $-24$.

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Key Concepts

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

Simplifying Expressions

To simplify expressions means making them easier to work with or understand. In algebra, this often involves reducing expressions to their simplest form. For example, when using the distributive property, we simplify by expanding an expression like $-2(5+7)$ by multiplying each term inside the parentheses by $-2$. Another simplification step is combining like terms. After distributing, $-2 imes 5$ and $-2 imes 7$ are combined, giving you $-10$ and $-14$ respectively. Finally, adding these gives us $-24$.
Here is a short guide to simplify expressions:

Identify terms and operations: Look for additions or subtractions that can be combined.
Apply properties: Use the distributive property where applicable.
Combine like terms: Group the similar things and add or subtract them.
Always check your work by simplifying any further if possible.

This process makes working with expressions easier, especially when solving equations.

Algebraic Expressions

Algebraic expressions are a combination of numbers, variables, and operations. They form the building blocks of algebra. Expressions such as $-2(5+7)$ are algebraic because they involve numbers and the multiplication operation. Understanding an algebraic expression's structure is crucial in simplifying and solving it.
Key parts of algebraic expressions involve:

Terms: Each part separated by a $+$ or $-$ sign, such as $-2$, $5$, $7$ .
Coefficients: The number that multiplies a variable, in this case, $-2$ is acting as a coefficient.
Operators: These are symbols like $+$, $-$, or $\times$ that define operations between terms.

Learning to recognize and manipulate these parts helps in simplifying and solving algebraic expressions effectively.

Basic Arithmetic Operations

Basic arithmetic operations form the foundation of solving algebraic problems. They include addition, subtraction, multiplication, and division. In the problem $-2(5+7)$, we use these operations to simplify the expression. Understanding how each operation works is essential.
Here's a breakdown of each operation:

Multiplication: Consists of repeated addition. For example, $-2 \cdot 5$ means adding $-2$ five times.
Addition: Brings two numbers together to form a sum, $-10 + (-14)$ adds two negative numbers, resulting in $-24$.
Subtraction: Could be seen as adding a negative number.
Division: Breaking a number into equal parts, less common in this context but still vital.

By mastering these operations and employing them in combination, like in this expression, we can simplify complex problems simply.

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91影视

Rewrite each expression using the distributive property. Simplify if possible. $$-2(5+7)$$

Short Answer

Step by step solution

Identify the terms

Apply the distributive property

Simplify the expression

Write the final answer

Key Concepts

Simplifying Expressions

Algebraic Expressions

Basic Arithmetic Operations

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