Basic Algebra
Fundamental algebraic formulas and identities.
Quadratic Formula
$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$
Solutions to ax² + bx + c = 0
Difference of Squares
$$a^2 - b^2 = (a+b)(a-b)$$
Factorization of difference of squares.
Perfect Square Trinomial
$$(a \pm b)^2 = a^2 \pm 2ab + b^2$$
Expansion of perfect squares.
Binomial Theorem
$$(a + b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k} b^k$$
General expansion of binomials.
Logarithm Properties
$$\log_a(xy) = \log_a(x) + \log_a(y)$$
$$\log_a\left(\frac{x}{y}\right) = \log_a(x) - \log_a(y)$$
Arithmetic Sequence
$$a_n = a_1 + (n-1)d$$
$$S_n = \frac{n}{2}(2a_1 + (n-1)d)$$
nth term and sum of arithmetic sequence.