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Chapter 1: Problem 783

Simplify using the distributive property. $$ 6(c-13) $$

Short Answer

Expert verified
6c - 78

Step by step solution

01

Identify the Terms Inside the Parentheses

Look at the expression inside the parentheses: Inside the parentheses, we have the term \( c - 13 \).
02

Apply the Distributive Property

The distributive property states that \( a(b + c) = ab + ac \). So distribute 6 to both terms inside the parentheses: \[ 6(c - 13) = 6 \cdot c + 6 \cdot (-13) \]
03

Perform the Multiplication

Multiply each term by 6: \[ 6 \cdot c = 6c \] \[ 6 \cdot (-13) = -78 \]
04

Write the Final Simplified Expression

Combine the results of the multiplications to form the final expression: \[ 6c - 78 \]

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Key Concepts

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

Simplifying Expressions
In mathematics, simplifying expressions is a crucial skill that makes problem-solving more efficient. It typically involves reducing an expression to its simplest form. Consider the expression we started with, \( 6(c - 13) \). To simplify, we use the distributive property. Simplifying can involve steps like combining like terms, performing arithmetic operations, and using properties of algebra.
Parentheses
Parentheses play a vital role in algebra. They indicate which operations should be performed first and help group terms together. In the expression \( 6(c - 13) \), the parentheses tell us to look inside and perform the operations inside them before anything else. Breaking it down:
  • Identify the terms: \(c - 13\)
  • Apply further operations governed by the distributive property
Parentheses ensure clarity and accuracy in mathematical expressions, helping avoid confusion.
Multiplication
Multiplication is one of the fundamental operations in algebra. When you apply the distributive property, you multiply each term inside the parentheses by the factor outside. Here鈥檚 what happens in our example:
  • Distribute the 6 to each term inside the parentheses: \( 6 \times c \) and \( 6 \times (-13) \)
  • Perform the multiplication: \( 6c \) and \( -78 \)
    The final expression \( 6c - 78 \) is a result of distributing and multiplying correctly. Understanding and practicing these operations are key to mastering algebra.

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