Question

Let's look at how the order of operations works with numbers.

Consider this numerical expression.

(2 + 3) − 4 · 6
First, we perform the operation in parentheses.

5 − 4 · 6
Next, we multiply.

5 − 24
Finally, we subtract.

-19
In the problem solved on this screen, could we have performed a different operation first, instead of adding 2 + 3 in parentheses?

Open the Notebook tool (), and write your answer.

We can apply the order of operations with polynomial operations as well. Let’s look at an example.

Answer 1

In the expression \( (2 + 3) − 4 \cdot 6 \), the order of operations dictates that we first solve the parentheses, then perform multiplication, and finally execute the subtraction.

To answer your question, we cannot perform a different operation first instead of adding \( 2 + 3 \) in parentheses. The parentheses indicate that this operation must be performed before any other operations. According to the order of operations (PEMDAS/BODMAS), operations in parentheses take precedence over multiplication and subtraction. Therefore, if we were to ignore the parentheses and look at the entire expression as is, the operations would yield a different result and not adhere to the established order.

To clarify, here’s how the expression works out when following the correct order of operations:

1. Solve within the parentheses: \( 2 + 3 = 5 \)
2. Next, multiply: \( 4 \cdot 6 = 24 \)
3. Finally, subtract: \( 5 - 24 = -19 \)

An example of applying order of operations with polynomials could involve simplifying an expression like \( 3(x + 2) - 4 + 2x \). The order of operations will guide you to first expand the polynomial, then combine like terms and continue simplifying. If you'd like to see a specific polynomial example, feel free to ask!