Problem 50 Simplify each expression. $$ ... [FREE SOLUTION]

Chapter 3: Problem 50

Simplify each expression. $$ -8(1+v)+6 v $$

Short Answer

Expert verified

The simplified expression is $-8 - 2v$.

Step by step solution

Distribute the -8

Apply the distributive property to the expression $-8(1+v)$ by multiplying each term inside the parentheses by -8. Perform the calculations as follows: $-8 \cdot 1 = -8$ $-8 \cdot v = -8v$ Thus, $-8(1+v) = -8 - 8v$.

Combine Like Terms

Take the expanded expression from Step 1, which is: $-8 - 8v$, and add $6v$ to it, giving us: $-8 - 8v + 6v$. Combine the like terms $-8v$ and $6v$ which results in: $-8v + 6v = -2v$. Hence, the expression becomes: $-8 - 2v$.

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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 key principle in algebra, allowing you to simplify expressions by removing parentheses. It essentially means that you distribute or "give out" a multiplier across terms inside parentheses. In our given problem, we use the distributive property on $-8(1 + v)$. Here's how it works, step-by-step:

You take the number outside the parentheses, which is $-8$, and multiply it by each term inside the parentheses.
First, multiply $-8$ by $1$. This results in $-8$.
Next, multiply $-8$ by $v$, giving $-8v$.

This step transforms $-8(1 + v)$ into $-8 - 8v$. This method ensures every term inside the grouping symbols is considered and properly distributed.

Combining Like Terms

Combining like terms is an essential step in simplifying algebraic expressions. It involves merging terms that share the same variable and power. This process reduces the complexity of the expression, making it easier to handle.Let's delve into the process using our example:

We have the expression $-8 - 8v + 6v$.
Identify the like terms: $-8v$ and $6v$, both containing the variable $v$.
Combine them by adding their coefficients: $-8 + 6$, which simplifies to $-2v$.

This leads the expression to become $-8 - 2v$ after combining the like terms. By doing this, we make the expression simpler and easier to evaluate.

Algebraic Expressions

An algebraic expression is a mathematical phrase that can include numbers, variables, and operators like plus or minus signs. Each part of an expression is considered a term, which could be a constant, a variable, or a coefficient tied to a variable.In our example, the original expression is $-8(1+v) + 6v$, containing numbers $-8$ and $6$, a variable $v$, and basic operations such as addition. Understanding algebraic expressions means recognizing:

Constants, which are numbers standing alone (e.g., $-8$).
Variables, which are symbols representing unknown values (e.g., $v$).
Coefficients, which are numbers multiplied by the variables (e.g., $-8$ in $-8v$).

Grasping these components aids in effectively simplifying and manipulating algebraic expressions.

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91影视

Simplify each expression. $$ -8(1+v)+6 v $$

Short Answer

Step by step solution

Distribute the -8

Combine Like Terms

Key Concepts

Distributive Property

Combining Like Terms

Algebraic Expressions

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