Algebra Fundamentals and Factoring Formulas

These flashcards cover essential algebra formulas including imaginary numbers, various factoring methods (cubes, squares, trinomials), exponent laws, and basic coordinate geometry formulas.

$i$ (Imaginary Unit)

The unit defined as $\sqrt{-1} = i$.

Conjugate rule

$$(a+b)(a-b) = a^2 - b^2$$

Sum of cubes formula

$$a^3 + b^3 = (a+b)(a^2 - ab + b^2)$$

Difference of squares

$$a^2 - b^2 = (a+b)(a-b)$$

Perfect square trinomial (Addition)

$$a^2 + 2ab + b^2 = (a+b)^2$$

Perfect square trinomial (Subtraction)

$$a^2 - 2ab + b^2 = (a-b)^2$$

Difference of cubes

$$a^3 - b^3 = (a-b)(a^2 + ab + b^2)$$

Quadratic Formula

$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$

Factoring by Grouping

A factoring method used when there are $4$ terms.

Product rule (Exponents)

$$a^m \times a^n = a^{m+n}$$

Quotient rule (Exponents)

$$\frac{a^m}{a^n} = a^{m-n}$$

Power rule (Exponents)

$$(a^m)^n = a^{mn}$$

Negative exponent rule

$$a^{-n} = \frac{1}{a^n}$$

Fractional exponents rule

$a^{1/2} = \sqrt{a}$, $a^{1/3} = \sqrt[3]{a}$, and $a^{m/n} = \sqrt[n]{a^m}$

Equation of a circle

$$(x-h)^2 + (y-k)^2 = r^2$$

Distance formula

$$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$

Slope

Defined in the notes as rise-rise, run-rub (commonly $\frac{\text{rise}}{\text{run}}$).