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Chapter 10: Problem 54

Simplify. $$ (8-2)(3-9) $$

Short Answer

Expert verified
-36

Step by step solution

01

Simplify each expression within the parentheses

First, simplify the expressions within the parentheses individually. For the expression \(8-2\), subtract 2 from 8 to get 6. For the expression \(3-9\), subtract 9 from 3 to get -6.
02

Substitute the simplified values back

After simplifying the expressions within the parentheses, substitute the simplified values back into the original expression. So, \(8-2\) becomes 6, and \(3-9\) becomes -6. This gives us \(6 \times -6\).
03

Multiply the simplified values

Finally, multiply the simplified values. Multiply 6 and -6 to get -36.

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Key Concepts

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

Order of Operations
Understanding the order in which mathematical operations should be performed is crucial. This standard procedure is known as the Order of Operations. The common acronym PEMDAS can help you remember the sequence:
  • P stands for Parentheses 鈥� First, solve expressions inside parentheses.
  • E stands for Exponents 鈥� Next, tackle any exponents (powers or roots).
  • MD stands for Multiplication and Division 鈥� Perform these from left to right.
  • AS stands for Addition and Subtraction 鈥� Lastly, carry these out from left to right.
In our exercise, we start with the parentheses: \((8-2)(3-9)\)
Always follow the steps in this order to ensure you simplify expressions correctly!
Subtraction
Subtraction plays a key role in simplifying expressions. Subtraction is taking away one value from another. Let's break it down using our exercise:
Step 1: Deal with the first parentheses, \(8-2\). Subtracting 2 from 8 results in 6.
Step 2: Now handle the second parentheses, \(3-9\). Here, you鈥檙e taking a larger number away from a smaller one, resulting in a negative number, -6.
Remember, subtraction can lead to positive or negative results, depending on the numbers involved. Negative results often come from subtracting a bigger number from a smaller one.
Multiplication
After simplifying within the parentheses, multiplication is the next step. This is combining multiple amounts together. Using our simplified expression, \(6 \times -6\):
  • When multiplying a positive and a negative number, the result is negative.
  • Here, 6 (positive) multiplied by -6 (negative) equals -36.
Understanding the signs is crucial in multiplication:
  • Positive 脳 Positive = Positive
  • Negative 脳 Negative = Positive
  • Positive 脳 Negative = Negative
So, always consider the signs when multiplying numbers.

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