Question

What are the coefficients for the binomial expansion of (p + q)6?

1, 8, 28, 56, 70, 56, 28, 8, 1
1, 6, 15, 20, 15, 6, 1
1, 5, 10, 10, 5, 1
1, 4, 6, 4, 1

Answer 1

Answer: B: 1, 6, 15, 20, 15, 6, 1

Answer 2

1, 6, 15, 20, 15, 6, 1

Explanation:

The binomial expansion of (p + q)⁶ gives 1, 6, 15, 20, 15, 6, 1.

There is always one more extra term for each power;

(p + q)⁰ = 1

(p + q)¹ = 1 1

(p + q)² = 1 2 1

(p + q)³ = 1 3 3 1

(p + q)⁴ = 1 4 6 4 1

(p + q)⁵ = 1 5 10 10 5 1

(p + q)⁶ = 1 6 15 20 15 6 1

The above is a paschal triangle and which shows the coefficients of the expanded terms to their power.