Algebra Formula Sheet and Exponent Rules

Flashcards covering linear equation formulas, special product formulas, domain/range definitions, and exponent rules.

Slope Intercept Form

$$y = mx + b$$

Point Slope Form

$$y - y_1 = m(x - x_1)$$

Slope Formula

$$\frac{y_2 - y_1}{x_2 - x_1}$$

Standard Form

$Ax + By = C$ [ $A$ must be positive, All must be whole numbers ]

Domain

X-Coords

Range

Y-Coords

Distance Formula

$$\text{Distance} = \text{Rate} \times \text{Time}$$

Vertical Line Slope

$$m = \text{undefined}$$

Horizontal Line Slope

$$m = \text{zero}$$

Special Product: $(a+b)^2$

$$a^2 + 2ab + b^2$$

Special Product: $(a-b)^2$

$$a^2 - 2ab + b^2$$

Special Product: $(a+b)(a-b)$

$$a^2 - b^2$$

Special Product: $(a+b)^3$

$$a^3 + 3a^2b + 3ab^2 + b^3$$

Special Product: $(a-b)^3$

$$a^3 - 3a^2b + 3ab^2 + b^3$$

Exponent Rules Chart

A reference guide detailing various exponent laws including zero power, unit power, product, quotient, power to a power, power of a product/quotient, negative exponents, and fractional exponents.

Exponent of Zero

$a^0 = 1$ if $a \neq 0$

Exponent of One

$$a^1 = a$$

Exponent Product

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

Exponent Quotient

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

Exponent Power

$$(a^m)^n = a^{m \times n}$$

Exponent Power of a Product

$$(a \times b)^m = a^m \times b^m$$

Exponent Power of a Quotient

$$\left(\frac{a}{b}\right)^m = \frac{a^m}{b^m}$$

Exponent Negative

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

Exponent Fractional

$$a^{\frac{a}{b}} = \sqrt[b]{a^a}$$

Factoring Cubics/Cube Formula: a³ + b³

(a+b)(a² - ab + b²)

Factoring Cubics/Cube Formula: a³ - b³

(a-b)(a² + ab + b²)

Difference of Two Squares: a²-b²

(a-b)(a+b)

Pythagorean Theorem

a² + b² = c²