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Chapter 6: Problem 189

Multiply. $$12 x(x-10)$$

Short Answer

Expert verified
12x(x-10) = 12x^2 - 120x

Step by step solution

01

Distribute the First Term

Multiply the first term 12x by both terms inside the parenthesis. This means you will distribute 12x to both x and -10 separately.
02

Multiply 12x by x

Multiply the term 12x by x: \[ 12x \times x = 12x^2 \]
03

Multiply 12x by -10

Multiply the term 12x by -10: \[ 12x \times (-10) = -120x \]
04

Combine the Results

Combine the results from Step 2 and Step 3: \[ 12x^2 - 120x \]

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Key Concepts

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

Distributive Property
To start with polynomial multiplication, we often use the Distributive Property. This property allows us to multiply a single term by each term inside parentheses. In our example, we have 12x multiplied by the expression (x-10). Here's how it works step-by-step:

First, take the term 12x and distribute it to both x and -10 inside the parentheses. This means:
  • Multiply 12x by x to get 12x2
  • Multiply 12x by -10 to get -120x
This step ensures that each term inside the parentheses is considered, making the polynomial multiplication thorough and accurate.
Combining Like Terms
After applying the Distributive Property, we need to combine like terms. This means adding or subtracting terms that have the same variable raised to the same power. Let's go back to our result from distribution:

We have:
  • 12x2
  • -120x
These terms are not like terms because they do not have the same variable power. Because 12x2 cannot be combined with -120x, the final form remains:

12x2 - 120x

Remember, only terms with identical variable parts can be combined, helping in simplifying algebraic expressions efficiently.
Algebraic Expressions
Understanding algebraic expressions is key. An algebraic expression combines numbers, variables, and operators (like +, -, 脳). For instance, in our example 12x(x-10), we have:
  • 12x as a single term
  • (x-10) as a binomial (two-term expression)
We use operations to manipulate these components:

After applying the Distributive Property and combining like terms, we simplify the expression to its most manageable form.
Remember, the goal is to understand each part of the expression and confidently apply the right operations to achieve the solution.

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Most popular questions from this chapter

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