Problem 31 - Elementary Algebra

Question

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

Step-by-Step Solution

Answer

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

Step 1: 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.

Step 2: 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: $$15(15)-4(56)$$

Step 3: 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: $$225-224$$

Step 4: 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: $$1$$.