Shortcut method to find out series in binomial theorem.

(x+y)⁰ = 1
(x+y)¹ = x + y
(x+y)² = x² + 2xy + y²
(x+y)³ = x³ + 3x²y + 3xy² + y³
(x+y)⁴ = x⁴ + 4x³y + 6x²y² + 4xy³ + y⁴
(x+y)⁵ = x⁵ + 5x⁴y + 10x³y² +10x²y³ + 5xy⁴ + y⁵

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

using binomial triangle.