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

Solution:

Given (p + q)6

Using binomial theorem, (x + a)n = 1 + nx + [n(n - 1)/2!] x2 + [n(n - 1)(n - 2)/3!] x3 +....

Here n = 6, x = p and a = q. Let us substitute in the binomial expansion formula.

(p + q)6= p6 + 6 × p5(q) + 15 × p4(q)2 + 20 × p3(q)3 + 15 × p2(q)4 + 6 × p(q)5 + (q)6

So, (p + q)6 = p6 + 6 × p5(q) + 15 × p4(q)2 + 20 × p3(q)3 + 15 × p2(q)4 + 6 × p(q)5 + (q)6

Therefore, all the coefficients in the binomial expansion are 1, 6, 15, 20, 15, 6, 1 

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

Summary:

The coefficients for the binomial expansion of (p + q)6 are 1, 6, 15, 20, 15, 6, 1.

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