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Chapter 6: Problem 179

Multiply. $$-3(k-4)$$

Short Answer

Expert verified
-3k + 12

Step by step solution

01

Distribute the -3

Multiply -3 by each term inside the parentheses. This means you multiply -3 by k and -3 by -4.
02

Multiply -3 by k

-3 times k is -3k.
03

Multiply -3 by -4

-3 times -4 is 12.
04

Combine the results

Write the results together to form the final expression. This gives us -3k + 12.

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Key Concepts

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

Understanding Multiplication in Algebra
Multiplication is a key operation in algebra that involves combining numbers or expressions. When dealing with algebraic expressions, multiplication follows specific rules to ensure accurate results. For example, consider the expression \(-3(k-4)\).

In this expression, the number -3 needs to be multiplied by both terms inside the parentheses. The distributive property allows us to do this effectively by spreading the multiplication over each term individually. Thus, we multiply -3 by \(k\) and multiply -3 by -4. This approach simplifies complex expressions and makes solving them manageable.

To recap:
  • Distribute -3 to \(k\).
  • Distribute -3 to -4.
Taking it step-by-step simplifies the process and leads to the correct solution.
Handling Algebraic Expressions
Algebraic expressions consist of variables, numbers, and operations. They represent quantities in general terms and can involve addition, subtraction, multiplication, or division. In our example, we have the expression \(-3(k-4)\).

Here鈥檚 how to handle such expressions:
  • Identify the terms: In \( -3(k-4) \), the terms are \( k \) and \( -4 \).
  • Use the distributive property to break down the expression properly before performing the operations.
  • Combine like terms to simplify.
This ensures each part of the expression is accurately accounted for, leading to the correct simplified form.
In our case, distributing gives us two separate products, \( -3k \) and \( -3 \times -4 \), which we then simplify and combine.
Working with Negative Numbers
Negative numbers can seem tricky, but with practice, they become more manageable. When multiplying negative numbers in algebraic expressions, it鈥檚 crucial to remember the signs rule:
  • A negative times a positive gives a negative result (\( -3 \times k = -3k \)).
  • A negative times a negative gives a positive result (\( -3 \times -4 = 12 \)).
In our example, \-3(k-4)\, we see both principles in action:
  • \( -3 \times k = -3k \)
  • \( -3 \times -4 = 12 \)
Understanding these rules helps to prevent mistakes and ensures accurate solutions. Practicing with multiple examples enhances confidence and proficiency in handling negative numbers in algebraic contexts.

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Most popular questions from this chapter

Handshakes At a company meeting, every employee shakes hands with every other employee. The number of handshakes is given by the expression \(\frac{n^{2}-n}{2},\) where \(n\) represents the number of employees. How many handshakes will there be if there are 10 employees at the meeting?

Divide each polynomial by the binomial. $$\left(x^{3}-216\right) \div(x-6)$$

Divide each polynomial by the binomial. $$\left(d^{2}+8 d+12\right) \div(d+2)$$

Simplify. (a) \(4^{-2}\) (b) \(10^{-3}\)

Divide each polynomial by the monomial. $$\frac{49 c^{2} d^{2}-70 c^{3} d^{3}-35 c^{2} d^{4}}{7 c d^{2}}$$
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