Problem 111 - Elementary Algebra

Question

\([10-3(2+7)+20]^{2}\)

Step-by-Step Solution

Answer

9

Step 1 - Simplify Inside the Parentheses

First, solve the expression inside the parentheses: \(2 + 7 = 9\)

Step 2 - Multiply Inside the Brackets

Next, substitute the result from Step 1 into the expression and multiply: \(3 \cdot 9 = 27\)

Step 3 - Subtract and Add Inside the Brackets

Now, continue simplifying inside the brackets: \(10 - 27 + 20\). Perform the subtraction first: \(10 - 27 = -17\), then add 20: \(-17 + 20 = 3\)

Step 4 - Raise to the Power

Finally, raise the result to the power of 2: \(3^{2} = 9\)

Key Concepts

parentheses in math

Understanding parentheses in math is crucial since they determine the order in which operations are performed. Parentheses are used to group parts of a mathematical expression that should be solved first.
For example, in the given exercise, we start with the innermost parentheses: \(2 + 7\).
Within these parentheses, we perform the addition first, giving us 9. Parentheses help clarify the sequence of operations and ensure we follow the correct order.
This is key to avoiding mistakes in more complex equations.

exponents

Exponents, also known as powers, are used to express repeated multiplication. When you see a number raised to a power, such as \(3^{2}\), it means that the number is multiplied by itself.
In the exercise, after simplifying the expression inside the brackets, we encounter \(3^{2}\).
This means we multiply 3 by itself: \(3 \times 3 = 9\). Exponents hugely simplify expressions, making it easier to work with large numbers or repeated multiplication.

basic arithmetic operations

Basic arithmetic operations are the foundation of math and include addition, subtraction, multiplication, and division.
In this exercise, we use these operations in conjunction with parentheses and exponents. Here’s how:

• Addition: Inside the parentheses, we add 2 and 7 to get 9.
• Multiplication: Next, we multiply 3 by 9.
• Subtraction: We subtract 27 from 10.
• Addition (again): Finally, we add 20 to -17.

Understanding how to correctly apply these operations step-by-step ensures accurate results in any math problem.
Breaking down each operation helps to avoid mistakes and clearly see each part of the equation.