One way of looking at Pascal’s triangle is through its connection to algebra. For example, expand (or remove the brackets around) the expression (1 + x)² = (1 + x)(1 + x) = 1 + 2x + x². The same can be done with a cube; for example, (1 + x)³ = (1 + x)(1 + x)(1 + x) = (1 + x)(1 + 2x + x²) = 1 + 3x + 3x² + x³; and even the expression (1 + x)⁴, which equals 1 + 4x + 6x² + 4x³ + x⁴.

The coefficients (the numbers in front of the x’s) in the results are the connection. For the first example, the coefficients are 1, 2, 1; for the second one, 1, 3, 3, 1; and for the last expression, the coefficients are 1, 4, 6, 4, 1. These, of course, are the third, fourth, and fifth lines from Pascal’s triangle.