How do I do the pascal's triangle?

Question

a^6 + 6a^5^b + 15a^4b^2 + 20a^3b^3 + 15a^2b^4 + 6ab^5 + b^6 = (a + b)

Answer 1

Set up the triangle starting with 1, and then 1 1 below that, and then add adjacent numbers by pairs to fill in the next line, always starting and ending with 1.  The 7th line gives the coefficients for (a + b)⁶.  What you provided is the binomial expansion of (a + b)⁶.

 

1

1 1

1 2 1

1 3 3 1

1 4 6 4 1

1 5 10 10 5 1

1 6 15 20 15 6 1