1. The problem is to simplify the expression $n(n-3)$ and understand the formula for the sum of interior angles of a polygon, $S = (n-2)180^\circ$. 2. First, simplify the expression $n(n-3)$ by distributing $n$: $$n(n-3) = n \times n - n \times 3 = n^2 - 3n$$ 3. The formula $S = (n-2)180^\circ$ calculates the sum of the interior angles of a polygon with $n$ sides. 4. For example, if $n=5$ (a pentagon), then: $$S = (5-2)180^\circ = 3 \times 180^\circ = 540^\circ$$ 5. This means the sum of the interior angles of a pentagon is $540^\circ$. 6. The expression $n(n-3)$ is often used to find the number of diagonals in a polygon, which is: $$\text{Number of diagonals} = \frac{n(n-3)}{2}$$ 7. For a pentagon ($n=5$), the number of diagonals is: $$\frac{5(5-3)}{2} = \frac{5 \times 2}{2} = 5$$ Final answers: - Simplified expression: $n^2 - 3n$ - Sum of interior angles: $S = (n-2)180^\circ$ - Number of diagonals: $\frac{n(n-3)}{2}$