1. Cheatsheet

1.1. Arithmetic Operations

1.2. Exponents and Radicals

1.3. Factoring Special Polynomials

${𝑥}^2-{𝑦}^2=\left(𝑥+𝑦\right)\left(𝑥-𝑦\right)$

${𝑥}^3+{𝑦}^3=\left(𝑥+𝑦\right)\left({𝑥}^2-𝑥𝑦+{𝑦}^2\right)$

${𝑥}^3-{𝑦}^3=\left(𝑥-𝑦\right)\left({𝑥}^2+𝑥𝑦+{𝑦}^2\right)$

1.4. Binomial Theorem

${\left(𝑥+𝑦\right)}^{𝑛}={\sum }_{𝑘=0}^{𝑛}\left[\begin{array}{c}𝑛\\ 𝑘\end{array}\right]{𝑥}^{𝑛-𝑘}{𝑦}^{𝑘}$

1.5. Quadratic Formula

If $𝑎{𝑥}^2+𝑏𝑥+𝑐=0$, then $𝑥=\frac{-𝑏\pm \sqrt{{𝑏}^2-4𝑎𝑐}}{2𝑎}$

1.6. Inequalities and Absolute Value

If $𝑎<𝑏$ and $𝑏<𝑐$, then $𝑎<𝑐$

If $𝑎<𝑏$, then $𝑎+𝑐<𝑏+𝑐$

If $𝑎<𝑏$ and $𝑐>0$, then $𝑐𝑎<𝑐𝑏$

If $𝑎<𝑏$ and $𝑐<0$, then $𝑐𝑎>𝑐𝑏$

If $𝑎>0$, then

$\left|𝑥\right|=𝑎\text{means}𝑥=𝑎\text{or}𝑥=-𝑎$

$\left|𝑥\right|<𝑎\text{means}-𝑎<𝑥<𝑎$

$\left|𝑥\right|>𝑎\text{means}𝑥>𝑎\text{or}𝑥<-𝑎$