Binomial Theorum

Expanding a binomial

Note:

n = the exponent

r = term # (0, 1, 2 … n)

a = first #, b = second #

Finding a term

Finding coefficient of a term

Term independent of variable

Sum of coefficients

Finding n from a terms value

Product rule

a^m × a^n = a^(m + n)
Example: x^3 × x^4 = x^7

Division rule

a^m ÷ a^n = a^(m - n)
Example: y^5 ÷ y^2 = y^

Power of a power rule

(a^m)^n = a^(m × n)
Example: (x^2)^3 = x^6

Power of a product rule

(a × b)^n = a^n × b^n
Example: (2x)^3 = 2^3 × x^3 = 8x^3

Power of a division rule

(a ÷ b)^n = a^n ÷ b^n
Example: (x ÷ 2)^3 = x^3 ÷ 8

Negative exponent rule

a^(-n) = 1 ÷ a^n
Example: x^(-3) = 1 ÷ x^3

Fraction rule

a^(1/n) = nth root of a
a^(m/n) = nth root of a^m
Example: 8^(2/3) = cube root of 8^2 = cube root of 64 = 4