Binomial Expansion Notes

Combinations

• Combinations: Counting options where order is NOT important.
• Combinations are unordered sets of $r$ objects taken from a set of $n$ distinct objects.
• $nCr$ represents combinations.

Pascal's Triangle

• Pascal's Triangle: Pattern named after Blaise Pascal.
• Numbers in each row are binomial coefficients.
• Pascal's triangle can be linked to the notation $\binom{n}{r}$.

Polynomials

• Polynomial: Expression where the power of every variable is a positive whole number.
• Degree: Highest power of the variable in a polynomial.
  • Linear polynomials have degree 1.
  • Quadratic polynomials have degree 2.
  • Cubic polynomials have degree 3.
• Leading term: Term containing the highest power of the variable.
• Monic polynomial: Polynomial where the coefficient of the leading term is 1.
• Constant term: Term that does not contain a variable.
• Factorial notation (!): Special case: $0!$