a. \( (1+x)^{2} \)

Did you know that the expression \( (1+x)^{2} \) can be expanded using the binomial theorem? This theorem states that \( (a+b)^{n} \) can be expressed as the sum of terms of the form \( C(n, k) a^{n-k} b^{k} \), where \( C(n, k) \) is the binomial coefficient. For our case, it expands to \( 1 + 2x + x^{2} \) – pretty neat! In real-world scenarios, the expression \( (1+x)^{2} \) can represent various situations such as project growth or interest on investments. If you take an initial amount and expect it to grow by a percentage \( x \) over a period, this expression helps you to calculate the total amount after that growth, highlighting its usefulness in finance and economics!