Evaluating a Binomial Expansion?

📌 CONCEPT: The binomial theorem is a mathematical concept that allows us to expand expressions of the form (a + b) raised to a positive integer power n.

📐 RULE / FORMULA: According to the binomial theorem, the expansion of (a + b)^n is given by the formula: ψ(n, r)a^(n-r)b^r, where r ranges from 0 to n, and ψ(n, r) represents the binomial coefficient.

💡 WORKED EXAMPLE: To find the coefficient of the term containing x^3 in the expansion of (x + 1/y)^9, we need to find the term where the power of x is 3. This corresponds to the term with r = 6, since 9 - 6 = 3. The binomial coefficient ψ(9, 6) is equal to 84. Therefore, the term containing x^3 is given by 84(x^3) * (1/y)^6 = 84x^3 / (y^6).

⚠️ COMMON MISTAKE: Students often confuse the binomial coefficient with the exponent of the term, leading to incorrect calculations.