QUESTION 2 Determine the products of the following and simplify where powstle \begin{tabular}{|l|l|l|}\hline 2.1 & \( x(1-x) \) \\ \hline\end{tabular}

Let's multiply \( x(1-x) \): distribute \( x \) across \( 1-x \). You'll get \( x \cdot 1 - x \cdot x \), which simplifies to \( x - x^2 \). So, the final, simplified expression is \( -x^2 + x \). Now, here's a fun fact: the expression \( x(1-x) \) actually represents a quadratic function, and its graph is a downward-opening parabola! This parabola crosses the x-axis at \( x=0 \) and \( x=1 \), making it very easy to spot its maximum value at \( x=\frac{1}{2} \), where it peaks at \( \frac{1}{4} \). When working with polynomials like this, a common mistake is forgetting to distribute correctly or to combine like terms. A good tip is to always double-check each term after expansion, ensuring that no negative signs or coefficients are overlooked! This will save you from embarrassing calculation errors!