Pascal's triangle

Rows.
- Row 0: $1$
- Row 1: $1\quad 1$
- Row 2: $1\quad 2\quad 1$
- Row 3: $1\quad 3\quad 3\quad 1$
- Row 4: $1\quad 4\quad 6\quad 4\quad 1$
- Row 5: $1\quad 5\quad 10\quad 10\quad 5\quad 1$
- Row 6: $1\quad 6\quad 15\quad 20\quad 15\quad 6\quad 1$

Coefficients of $(a+b)^5$. $1,5,10,10,5,1$.

Conclusion. $(a+b)^5=a^5+5a^4b+10a^3b^2+10a^2b^3+5ab^4+b^5$.