Problem 67 Simplify each expression. $$ ... [FREE SOLUTION]

Chapter 3: Problem 67

Simplify each expression. $$ 3 a+4(a+3) $$

Short Answer

Expert verified

The simplified expression is $ 7a + 12 $.

Step by step solution

Expand the Expression

Begin by expanding the expression given inside the parentheses. The original expression is:\[ 3a + 4(a + 3) \]Use the distributive property to expand:\[ 4 \times a + 4 \times 3 = 4a + 12 \]

Combine Like Terms

Substitute the expanded terms back into the original expression:\[ 3a + 4a + 12 \]Now, combine the like terms, which are the terms with 'a'.\[ (3a + 4a) + 12 = 7a + 12 \]

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Key Concepts

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

Understanding the Distributive Property

The distributive property is a fundamental concept in prealgebra that helps simplify expressions by eliminating parentheses. It is used to distribute a single term across multiple terms inside parentheses. In our example, we start with the expression $ 3a + 4(a + 3) $. To apply the distributive property here, we distribute the number 4 across each term inside the parenthesis.

This means multiplying 4 by each term within the parentheses: $ 4 \times a $ and $ 4 \times 3 $.
So, the expression $ 4(a + 3) $ simplifies to $ 4a + 12 $.

By applying the distributive property, we've removed the parentheses from our expression and simplified it to make further operations easier.

Combining Like Terms

Once we've expanded the expression using the distributive property, our next step involves combining like terms. Like terms are terms that have identical variable parts. In our expanded expression $ 3a + 4a + 12 $, the like terms are $ 3a $ and $ 4a $.

To combine these terms, simply add their coefficients (the numerical parts): $ 3 + 4 $.
This results in $ 7a $.

After combining these terms, the expression simplifies to $ 7a + 12 $. Remember, this process is essential as it reduces the complexity of the expression, making it easier to understand and solve.

Expression Simplification

Expression simplification is the process of condensing a mathematical expression into its simplest form. When simplifying expressions like $ 3a + 4(a + 3) $, the goal is to make the expression as straightforward as possible without changing its value.Often, simplification involves:

Using the distributive property to expand terms and remove parentheses.
Combining like terms to reduce the expression further.

After these steps, expressions are easier to handle and provide clarity. In our example, the final simplified expression is $ 7a + 12 $, which is concise and ready for any further calculations. Remember, a simplified expression is always more manageable and less prone to errors.

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91影视

Simplify each expression. $$ 3 a+4(a+3) $$

Short Answer

Step by step solution

Expand the Expression

Combine Like Terms

Key Concepts

Understanding the Distributive Property

Combining Like Terms

Expression Simplification

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