Problem 206 Multiply. $$(8 j-1) j$$... [FREE SOLUTION]

Chapter 6: Problem 206

Multiply. $$(8 j-1) j$$

Short Answer

Expert verified

8j^2 - j

Step by step solution

Distribute the Term

Apply the distributive property by multiplying each term in the parenthesis by the variable outside. Here, multiply each term inside (8j-1) by j.

Multiply First Term

First, calculate (8j) \times j: \[8j \times j = 8j^2\]

Multiply Second Term

Next, calculate (-1) \times j: \[(-1) \times j = -j\]

Combine the Results

Finally, combine the results from the multiplication operations: \[8j^2 - j\]

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Key Concepts

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

Multiplying Binomials

Multiplying binomials is a key algebraic method where you simply multiply each term in one binomial by each term in the other binomial. Think of it as distributing each part separately and then combining the results. For example, to multiply $8j - 1$ by $j$, you need to individually multiply both $8j$ and $-1$ by $j$.

The process involves applying the distributive property twice.
This ensures all terms are properly multiplied and accounted for.

This technique is not limited to binomials with only variables. Sometimes, you might have 鈥榗onstant鈥� terms (numbers without variables) that need the same careful treatment.

Distributing Variables

When you encounter an algebraic expression where a variable needs to be distributed, the distributive property is your best friend. Here鈥檚 how it works step by step:

Start by identifying the terms inside the parenthesis that need to be multiplied by the variable or number outside the parenthesis.
Multiply each term inside the parenthesis by this 鈥榦utside鈥� term one by one.

For the given exercise, you distribute $j$ to both terms inside $8j-1$.
For example:

$8j \times j = 8j^2$
$-1 \times j = -j$

This step-by-step approach ensures no term is left out and each is treated individually before combining the results.

Combining Like Terms

Combining like terms helps simplify an algebraic expression to its smallest form. To do this correctly, follow these steps:

Identify terms that have the same variable raised to the same power.
Add or subtract the coefficients of these terms (the numbers in front of the variables).

In the case of our problem, you dealt with $8j^2$ and $-j$. After distributing and simplifying, you don't need to combine further because the terms $8j^2$ and $-j$ are not like terms. Like terms must have the same variable part, so $j^2$ and $j$ can't be combined.
Understanding how to combine like terms is vital for cleaning up and solving more complex algebraic expressions efficiently.

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91影视

Multiply. $$(8 j-1) j$$

Short Answer

Step by step solution

Distribute the Term

Multiply First Term

Multiply Second Term

Combine the Results

Key Concepts

Multiplying Binomials

Distributing Variables

Combining Like Terms

One App. One Place for Learning.

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