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Chapter 10: Problem 176

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

Short Answer

Expert verified
8b^2 - b

Step by step solution

01

Identify the Expression

The given expression to be multiplied is \( (8b - 1)b \)
02

Distribute b

To multiply, distribute the term \( b \) across the terms inside the parenthesis. This means you will multiply \( b \) by both \( 8b \) and \( -1 \).
03

Multiply b by 8b

First, multiply the term \( b \) by \( 8b \). This gives \( (8b \times b = 8b^2) \).
04

Multiply b by -1

Next, multiply the term \( b \) by \( -1 \). This gives \( (b \times -1 = -b) \).
05

Combine Like Terms

Now, combine the results from the previous steps: \( 8b^2 - b \). The final expression is \( 8b^2 - b \).

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Key Concepts

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

Algebraic Expressions
An algebraic expression combines numbers, variables (like $$b$$), and operators (such as + or -) into a mathematical phrase. Unlike equations, algebraic expressions do not have an equals sign. In our exercise, the expression is $$ (8b - 1)b $$. Understanding algebraic expressions is crucial because they lay the foundation for learning more complex math concepts.
Multiplying Terms
Multiplying terms inside an algebraic expression involves using the distributive property. This means you multiply each term inside the parentheses by the term outside. Let's break it down with our example:

Step 1: The given expression is $$ (8b - 1)b $$.
Step 2: Distribute the $$ b $$ term to both terms inside the parentheses.
Step 3: Multiply $$ b $$ by each term:
  • First, $$ 8b \times b $$ gives us $$ 8b^2 $$.
  • Next, $$ b \times -1 $$ gives us $$ -b $$.
This results in $$ 8b^2 - b $$.
Combining Like Terms
After multiplying the terms, the next step is to combine like terms, which are terms with the same variables raised to the same power. In our example, we have two terms: $$ 8b^2 $$ and $$ -b $$. These terms are already in their simplest form because they do not share the same power of $$ b $$. So, the final expression remains $$ 8b^2 - b $$.

When combining like terms, be sure to:
  • Identify terms with the same variable and exponents.
  • Add or subtract the coefficients of these terms.
This skill helps to simplify expressions, making them easier to work with in more complex problems.

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