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Chapter 1: Problem 31

For the following problems, use the order of operations to find each value. $$(10+5)(10+5)-4(60-4)$$

Short Answer

Expert verified
Question: Using the order of operations, simplify the following expression: \((10+5)(15)-4(60-4)\). Answer: The simplified expression is $$1$$.

Step by step solution

01

Parentheses/Brackets

First, we need to simplify the expression inside the parentheses. There are two sets of parentheses that we need to simplify: 1. \((10+5)\) 2. \((60-4)\) After we simplify these two sets of parentheses, we can move on to the next operation in the order of operations list.
02

Simplify the Expression Inside the Parentheses

Now, let's simplify the expressions inside the parentheses: 1. \((10+5)\) becomes \(15\) 2. \((60-4)\) becomes \(56\) Our new expression will be: $$15(15)-4(56)$$
03

Multiplication

Now we will perform the multiplication operation that we see in the expression. 1. \(15(15)\) becomes \(225\) 2. \(4(56)\) becomes \(224\) Our updated expression: $$225-224$$
04

Subtraction

Finally, perform the subtraction operation: $$225-224 = 1$$ Now that we have simplified the entire expression by following the order of operations, we have the final value: $$1$$.

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