PASCAL'S TRIANGLE
If a row in the triangle is represented by 1 a b c ...
the rule for creating the next row is:
1 1+a a+b b+c ...
The first and last numbers on each row are 1s.
So the triangle up to the 7th row (which we need for this question) is:
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
1 7 21 35 35 21 7 1. This is the row we need to expand (x+y)7:
x7+7x6y+21x5y2+35x4y3+35x3y4+21x2y5+7xy6+y7