Meet Pascal Triangle

Pascal’s Triangle is used to expand binomials.

(x + y)^n = Sum of (k=0 to n) C(n , k) x^(n — k) y^k

Combination C(n , k) = n ! / ( k ! (n — k) ! )

We use the Pascal Triangle

……….1

………1…1

…….1..2..1

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…..1..3..3..1

….1..4..6..4..1

..1..5.10.10.5..1

Examples: (Don’t use the top 1)

(x + y)² = x² + 2xy + y² Go to row 2 get 1 2 1

(x + y)⁴ = x⁴ + 4x³ y + 6x² y² + 4xy³ + y⁴

Go to row 4 get 1 4 6 4 1

How to get row 6

Row 5 is..1..5.10.10.5..1

Row 6 is..1 (1 +5) (5+10) (10 +10) (10+5) (5+1) 1

1 6 15 20 15 6 1

Please enjoy and have fun! Thank you!