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Chapter 6: Problem 207

Multiply. $$(w-6) \cdot 8$$

Short Answer

Expert verified
The product is \[8w - 48\].

Step by step solution

01

Distribute the 8

In this step, use the distributive property to multiply 8 by each term inside the parenthesis. So, we multiply 8 by both 'w' and '-6'.
02

Multiply 8 by w

First, multiply 8 by the variable 'w'. This gives us: \[8w\]
03

Multiply 8 by -6

Next, multiply 8 by -6. This gives us: \[8 \times -6 = -48\]
04

Combine the results

Combine the results from the previous steps. The expression becomes: \[8w - 48\]

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Key Concepts

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

Multiplication of Variables
Multiplying variables can seem tricky, but it's easier than you might think. Imagine you have a variable, like \(w\), and you want to multiply it by a number. In algebra, when you see something like \(8w\), it simply means 8 times \(w\).
This concept is key when you're working with algebraic expressions.

Let鈥檚 break it down. If you have an expression like \( 8 \times w \), you first write it as just \(8w\). Whether \(w\) equals 2, 3, or any other number, you just multiply that number by 8 to get your result. Easy, right?

Keep practicing this concept to get more comfortable. Remember, once you master multiplying with variables, other algebra topics will become simpler.
Algebraic Expressions
Algebraic expressions are a combination of numbers, variables (like \(w\)), and operations (such as addition or multiplication). In the problem \((w-6) \cdot 8\), we're dealing with an expression inside parentheses and a number outside.

Here's how to handle it step-by-step:
  • First, you'll use the distributive property. This means you multiply 8 by each term inside the parentheses.
So, the expression \( (w-6) \cdot 8 \) becomes \( 8w - 48 \).

The beauty of algebra is that it lets us work with unknown values until we get more information! But for now, understanding expressions is a crucial skill.
Combining Like Terms
Combining like terms helps simplify algebraic expressions. It's an important step in solving equations. In our example, we didn't need to combine terms because they were already simplified. But in many problems, you'll need this skill.

Here's a quick guide:
  • Like terms are terms that have the same variable raised to the same power. For example, \(8w\) and \(-3w\) are like terms, but \(8w\) and \(8w^2\) are not.
  • To combine like terms, add or subtract the coefficients (the numbers in front of the variables).
For instance, combining \(8w\) and \(-3w\) gives you \(5w\).

Practicing this will make your algebra journey much simpler. Always look out for like terms in your expressions and equations!

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Most popular questions from this chapter

Divide each polynomial by the monomial. $$\frac{66 x^{3} y^{2}-110 x^{2} y^{3}-44 x^{4} y^{3}}{11 x^{2} y^{2}}$$

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

Simplify. (a) \(3 \cdot 5^{-1}\) (b) \((3 \cdot 5)^{-1}\)

Divide each polynomial by the monomial. $$\frac{36 p^{3}+18 p^{2}-12 p}{6 p^{2}}$$

Divide the monomials. $$\frac{\left(10 m^{5} n^{4}\right)\left(5 m^{3} n^{6}\right)}{25 m^{7} n^{5}}$$
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