Pascal's Triangle
The Basics
\((a+b)^n\)
- \((a+b)^{1}= a+b\)
- \((a+b)^{2}= a^2+2ab+b^2\)
- \((a+b)^{3}= a^3+3a^2b+3ab^2+b^3\)
- \((a+b)^4=a^4+4a^3b+6a^2b^2+4ab^3+b^4\)
- \((a+b)^5=a^5+5a^4b+10a^3b^2+10a^2b^3+5ab^4+b^5\)
Example
\((2x+3)^5\)
Subsitute in:
- \((2x^5) + 5(2x)^4(3)+10(2x)^3(3)^2+10(2x)^2(3)^3+5(2x)(3)^4+3^5\)
Expand:
- \(32x^5+240x^4+720x^3+1080x^2+810x+243\)
Example with negetives
\((3-x)^4\)
Subsitute in:
- \(3^4+4(3)^3(-x)+6(3)^2(-x)^2+4(3)^1(-x^3)+(-x^4)\)
Expand:
- \(81-108x+54x^2-12x^3+x^4\)
