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Chapter 0: Problem 37

Simplify each expression. $$ 10-(4 y+8) $$

Short Answer

Expert verified
2 - 4y

Step by step solution

01

Distribute the negative sign inside the parentheses

Start by distributing the negative sign to each term inside the parentheses:
02

Combine like terms

Combine the constants (10 and -8) to simplify the expression: 10 - 8 - 4y This is equal to 2 - 4y, which is the simplified form.

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Key Concepts

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

Distributive Property
The distributive property helps us to handle expressions involving parentheses. It states that for any numbers a, b, and c: \(a(b + c) = ab + ac\). In simpler terms, you multiply each term inside the parentheses by the term outside.

In our exercise, we apply this to the negative sign (which can be thought of as -1) next to the parentheses.
For example:
  • If you have \(10 - (4y + 8)\), you distribute the -1: \(10 - 4y - 8\)
This step ensures every term inside the parentheses has been subtracted.
Like Terms
Like terms are terms that have the same variable raised to the same power. For example, in the expression \(10 - 4y - 8\), 10 and -8 are constants (numbers without variables), and -4y is a term with the variable y.

  • You can combine like terms to simplify the expression further.
  • Combine the constants (numbers) by simply adding or subtracting them.
Here, combine 10 and -8 to get 2.
This gives us the expression: \(2 - 4y\).
Always look for like terms to make your expressions simpler and easier to work with.
Simplification Process
Simplifying an expression means making it as simple as it can be. This often involves a few key steps:

  • First, use the distributive property to remove parentheses.
  • Then, combine like terms to condense the expression.

Let's look at the step-by-step simplification of our example:

  • Start with the expression: \(10 - (4y + 8)\)
  • Distribute the negative sign: \(10 - 4y - 8\)
  • Combine like terms: 10 and -8 to get \(2 - 4y\)
This results in the simplified expression: \(2 - 4y\).
Each step makes the expression easier to understand and solve.

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Most popular questions from this chapter

The distributive property can be used to mentally perform calculations. $$\begin{array}{l}38 \cdot 17+38 \cdot 3 \\\=38(17+3) \\\=38(20) \\\=760\end{array} $$Use the distributive property to calculate each value mentally. $$ 58 \cdot \frac{3}{2}-8 \cdot \frac{3}{2} $$

Write each percent as a fraction. Give answers in lowest terms. See Example 13. $$ 51 \% $$

Simplify each expression. $$ 10-2^{2}+9-(1-8) $$

Evaluate each expression for \(w=4, x=-\frac{3}{4}, y=\frac{1}{2},\) and \(z=1.25 .\) $$ x y+y^{4} $$

Evaluate each expression for \(a=-3, b=64,\) and \(c=6 .\) $$ 2(a-c)^{2}-a c $$
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