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.