Question

which row of pascal’s triangle corresponds to the coefficients of ((x + y)^7)?

○ a. 1, 6, 15, 20, 15, 6, 1

○ b. 1, 7, 21, 35, 35, 21, 7, 1

○ c. 1, 5, 10, 10, 5, 1

○ d. 1, 4, 6, 4, 1

Explanation:

Step1: Recall Pascal's Triangle Rule

The \(n\)-th row (starting from \(n = 0\)) of Pascal's Triangle gives the coefficients of \((x + y)^n\). For \((x + y)^7\), we need the 7th row (since \(n=7\), row index is \(n\)).

Step2: Analyze Each Option

• Option a: \(1, 6, 15, 20, 15, 6, 1\) is the 6th row (for \((x + y)^6\)).
• Option b: \(1, 7, 21, 35, 35, 21, 7, 1\) has 8 elements (since row \(n\) has \(n + 1\) elements; \(n = 7\) gives \(8\) elements), matching the coefficients of \((x + y)^7\).
• Option c: \(1, 5, 10, 10, 5, 1\) is the 5th row (for \((x + y)^5\)).
• Option d: \(1, 4, 6, 4, 1\) is the 4th row (for \((x + y)^4\)).

Answer:

b. 1, 7, 21, 35, 35, 21, 7, 1