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Chapter 5: Problem 2

Remove the brackets from the given expression: \(7(2 x+y)\)

Short Answer

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Question: Remove the brackets from the given expression: \(7(2x+y)\) Answer: \(14x + 7y\)

Step by step solution

01

Identify the terms inside the brackets

In the expression \(7(2x+y)\), we have two terms inside the brackets: \(2x\) and \(y\).
02

Distribute the constant outside the brackets

Apply the distributive property to the expression: \(7(2x+y) = 7*(2x) + 7*(y)\).
03

Simplify the expression

Multiply the constant with each term: \(7*(2x) = 14x\) and \(7*(y) = 7y\). So, the simplified expression is \(14x + 7y\).

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Key Concepts

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

Algebraic Expression
An algebraic expression is a combination of numbers, variables, and mathematical operations like addition, subtraction, multiplication, and division. These expressions are a fundamental part of algebra and allow us to represent real-world scenarios using symbols. For example, in the expression \(7(2x + y)\), the components are:
  • 7 - This is a constant multiplier.
  • 2x + y - This portion inside the brackets is an expression with terms.
  • 2x and y - These are terms, where x and y are variables.
Understanding the structure of algebraic expressions is crucial for solving problems. Identifying terms involves recognizing parts of the expression separated by plus or minus signs.
Simplification Process
The simplification process involves reducing an algebraic expression to its simplest form. This usually means eliminating brackets and combining like terms. In the given exercise, we needed to simplify \(7(2x + y)\). The steps involved were:
  • Removing Brackets: We used the distributive property to multiply the term outside the brackets with each term inside. This meant taking \(7\) and applying it to \(2x\) and \(y\).
  • Combining Multiplications: Multiplying \(7\) by each term gives us \(14x\) and \(7y\).
By following these steps, the original expression \(7(2x + y)\) is simplified to \(14x + 7y\). The simplification process makes expressions easier to handle, especially in further mathematical operations or equations.
Mathematical Operations
Mathematical operations in algebra include a range of basic calculations like addition, subtraction, multiplication, and division. They are used to manipulate variables and constants to achieve the desired form of an expression. In the context of the original exercise, the main operation used was multiplication, specifically through:
  • Distributive Property: This property allows us to multiply a single term across a sum or difference inside brackets. In \(7(2x + y)\), we multiplied \(7\) by both \(2x\) and \(y\).
  • Expression Multiplication: This involves distributing the multiplier \(7\) to each term inside the brackets, yielding \(7 \times 2x = 14x\) and \(7 \times y = 7y\).
Understanding these operations is key in algebra because they form the basis for solving and simplifying expressions, where we break down and reassemble components using established mathematical rules.

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