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Chapter 1: Problem 295

Simplify each expression. $$ (-3)^{2}-24 \div(8-2) $$

Short Answer

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5

Step by step solution

01

Calculate the Square

First, calculate the square of (-3), which is (-3)^2. You get 9 because (-3)*(-3)=9.
02

Simplify Inside the Parentheses

Next, simplify the expression inside the parentheses. (8-2) results in 6.
03

Perform the Division

Then divide 24 by the result from the previous step. 24 / 6 equals 4.
04

Subtract

Finally, subtract the result of the division from the result of the square. 9-4 results in 5.

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Key Concepts

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

Order of Operations
One of the most important concepts in solving algebra problems is the order of operations. This is the sequence in which you solve parts of an expression. The correct order to follow is known by the acronym PEMDAS, which stands for:
  • P: Parentheses
  • E: Exponents (or powers)
  • MD: Multiplication and Division (from left to right)
  • AS: Addition and Subtraction (from left to right)

For example, in the expression \((-3)^2 - 24 \div (8 - 2)\), we first calculate anything inside parentheses (8-2), then handle exponents \((-3)^2\). After that, we perform any multiplication or division (24 \div 6), and finally, we handle addition or subtraction (9 - 4). By following PEMDAS, we ensure the expression is solved correctly.
Squaring Numbers
Another essential concept in algebra is understanding how to square numbers.

Squaring a number means multiplying the number by itself. The notation for squaring a number is using an exponent of 2, such as \((-3)^2\).

Let's break this down:
  • The base is -3.
  • The exponent is 2.
  • \((-3)^2\) means (-3) \times (-3). The result is 9.

Remember that when you square a negative number, the result is positive because the product of two negative numbers is positive. So, \( (-3) \times (-3) = 9 \). This is one of the trickiest parts of squaring numbers. Make sure to always watch your signs!
Simplifying Expressions
Simplifying expressions involves combining like terms and reducing an expression to its simplest form.

Consider the final expression provided in the problem: \((-3)^2 - 24 \div (8 - 2) \). Simplifying expressions often involves multiple steps:
  • First, handle any operations inside parentheses: (8 - 2) = 6.
  • Then, address any exponents: \((-3)^2\) = 9.
  • Next, perform division: 24 \div 6 = 4.
  • Finally, perform the subtraction: 9 - 4 = 5.

By following these steps and carefully combining like terms, you simplify the expression to its most compact form. Simplifying not only makes expressions easier to work with but also helps in understanding the relationships between different terms and components within the expression.

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