Problem 68 Simplify each expression. $$ ... [FREE SOLUTION]

Chapter 3: Problem 68

Simplify each expression. $$ b+2(b-5) $$

Short Answer

Expert verified

The simplified expression is $ 3b - 10 $.

Step by step solution

Apply the Distributive Property

The expression is given as $ b + 2(b - 5) $. To simplify, start by distributing the $ 2 $ across the terms inside the parentheses $ (b - 5) $. Multiply $ 2 $ by both $ b $ and $ -5 $. This results in $ 2 \times b = 2b $ and $ 2 \times (-5) = -10 $. Thus, the expression becomes $ b + 2b - 10 $.

Combine Like Terms

Now, simplify the expression by combining like terms. The like terms in the expression $ b + 2b - 10 $ are $ b $ and $ 2b $. Add $ b + 2b $ to get $ 3b $. The expression simplifies to $ 3b - 10 $.

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Key Concepts

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

Distributive Property

The distributive property is a fundamental principle in algebra that helps simplify expressions by eliminating parentheses. It states that for any numbers or variables, $a(b + c) = ab + ac$. This means you will distribute or "pass" $a$ to each term inside the parentheses.

Begin with multiplying the outside term with each term inside the parentheses individually.
This method is helpful in breaking down complex expressions into simpler parts.

In our original exercise, we used the distributive property to simplify $2(b - 5)$. By distributing the $2$, we found that $2 \times b = 2b$ and $2 \times (-5) = -10$. Just like that, parentheses disappeared, and the expression morphed into $b + 2b - 10$. Remembering this property lets you tackle many algebraic problems easily.

Combining Like Terms

Combining like terms is the next step after using the distributive property. When we have an algebraic expression, we often have multiple terms sharing the same variable part, meaning they can be added or subtracted together.

Look for terms that have the same variable portion and the same exponent.
Constant terms, which do not have any variables, can also be combined with other constant terms.

In our problem, after applying the distributive property, we ended up with the expression $b + 2b - 10$. Both $b$ and $2b$ are like terms because they share the same variable "b". By adding them, we get $3b$. The expression then simplifies to $3b - 10$. This step effectively lends clarity and simplicity to algebraic solutions.

Algebraic Expressions

An algebraic expression is a mathematical phrase combining numbers, variables, and operations. Unlike a full equation, it doesn't include an equal sign. Understanding this concept is crucial as it鈥檚 the foundation of algebra.

Components of an expression include constants, variables, coefficients, and operators.
Expressions can be simplified but not solved, as there is no equality to determine a specific value for the variable.

In our original exercise $b + 2(b - 5)$, we are working with an algebraic expression. The goal is to simplify it using algebraic rules like the distributive property and combining like terms. Mastery of algebraic expressions allows you to manipulate and understand various mathematical models more effectively.

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91影视

Simplify each expression. $$ b+2(b-5) $$

Short Answer

Step by step solution

Apply the Distributive Property

Combine Like Terms

Key Concepts

Distributive Property

Combining Like Terms

Algebraic Expressions

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