Problem 94 Simplify. $$(10-7 b) 2$$... [FREE SOLUTION]

Chapter 4: Problem 94

Simplify. $$(10-7 b) 2$$

Short Answer

Expert verified

The simplified version of the provided expression is $20 - 14b$.

Step by step solution

Apply the Distributive Property

The distributive property allows us to eliminate the brackets by multiplying every term inside the bracket by the term outside the bracket. Thus, the expression breaks down to $2 * 10 - 2 * 7b$.

Perform Multiplication

Next, perform the multiplication operations. This gives $20 - 14b$.

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Key Concepts

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

Simplifying Expressions

Simplifying expressions is a key skill in algebra that involves reducing an expression into its most basic form. It makes working with expressions much easier, particularly as the equations become more complex. Let's look at the expression given:

- $(10 - 7b) \cdot 2$**Steps to Simplify**:

Understand the operation: The expression tells us that we need to multiply two factors, 2, and the entire bracket, $(10 - 7b)$.
Apply the distributive property: By distributing 2 to each term in the parenthesis, we simplify the expression.

This process makes the expression easier to handle and solve in any future calculations.

Basic Algebra

Basic Algebra is foundational in mathematics, dealing with symbols and the rules for manipulating those symbols. It allows us to express general mathematical concepts and solve equations easily. In this exercise, we encounter algebraic expressions and need to manipulate them.

**Key Ideas** in Basic Algebra include:

Using variables: Letters (like $b$ in the expression) that stand for unknown or changeable values.
Expressions and equations: Combinations of numbers and variables linked by operations.
Rules of operations: Following operations like addition, subtraction, multiplication, and division.

Understanding these basics helps us execute operations smoothly, like using the distributive property here.

Multiplication in Algebra

Multiplication in Algebra not only involves numbers but also variables. It is an essential part of simplifying expressions. In our example, multiplication is primarily carried out between the number 2 and the terms inside the parenthesis.

**Steps with Multiplication**:

Identify and multiply: Start by identifying the multiplier (in this case, 2) and multiply it with each term inside the brackets.
Combine results: After multiplying individually, combine the results to simplify the overall expression. For $2 \times 10$ we get 20, and for $2 \times -7b$, we get $-14b$.

This process of distributing and multiplying is a core algebraic skill, reducing expressions to simpler forms for further simplification or solving.

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91影视

Simplify. $$(10-7 b) 2$$

Short Answer

Step by step solution

Apply the Distributive Property

Perform Multiplication

Key Concepts

Simplifying Expressions

Basic Algebra

Multiplication in Algebra

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