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Using Pascal's Triangle for Expanding Expressions

Wednesday, 15 April 2026

Using Pascal’s triangle (or the binomial equation), you can quickly expand an equation such as (x+h)x(x+h)^x.

Pascal Triangle N=1,8.png

To do this you:

  1. Look at the nn-th row of the triangle (counting the very top 1 as row 0).
  2. First term (xx): Its power starts at nn and counts down to 0.
  3. Its power starts at 0 and counts up to nn.

Example

(x+h)3(x+h)^3 becomes 1x3+3x2h1+3x1h2+1h31x^3 + 3x^2h^1 + 3x^1h^2 + 1h^3, cleanly written as x3+3x2h+3xh2+h3x^3 + 3x^2h + 3xh^2 + h^3.