Compare Expressions: -2(3)² vs -(−6)² | Order of Operations Challenge

Which is larger?

$-2\cdot(3)^2⬜-(-6)^2$

To solve this problem, we'll follow these steps:

• Step 1: Evaluate the expression $-2 \cdot (3)^2$.
• Step 2: Evaluate the expression $-(-6)^2$.
• Step 3: Compare the results of Step 1 and Step 2.

Now, let's work through each step:

Step 1: Calculate $-2 \cdot (3)^2$.

First, find $(3)^2$. Since $3^2 = 9$, we have:

$-2 \cdot (3)^2 = -2 \cdot 9 = -18$.

Step 2: Calculate $-(-6)^2$.

First, find $(-6)^2$. Calculating the square gives:

$(-6)^2 = 36$.

Apply the negative sign: $-(-6)^2 = -36$.

Step 3: Compare the results.

We have $-2 \cdot (3)^2 = -18$ and $-(-6)^2 = -36$.

Since $-18$ is larger than $-36$, we conclude:

The expression $-2 \cdot (3)^2$ is greater than $-(-6)^2$.

Therefore, the solution to the problem is $>$.