Binomial Expression and Expansion Using Pascal's Triangle

Binomial Expression and Expansion Using Pascal's Triangle

This lesson covers the following key concepts:

• Binomial expression (x + y)ⁿ
• Pascal's triangle construction and pattern
• Expansion of (x + y)ⁿ using Pascal's triangle
• Finding coefficients from Pascal's triangle
• Properties of Pascal's triangle
• Number of terms in expansion
• Basic binomial expansions for small n

Important Formulas

• (x + y)^n = \sum_{r=0}^{n} ^nC_r x^{n-r} y^r
• $$\text{Pascal's triangle: each entry = sum of two above}$$
• $$\text{Row } n \text{ gives coefficients of } (x+y)^n$$
• $$\text{Number of terms} = n + 1$$
• $$^nC_r = ^{n-1}C_{r-1} + ^{n-1}C_r \text{ (Pascal's identity)}$$