1. Symbolab polynomial essay

# Symbolab polynomial essay

## Expand Rules

-(a\pm b)=-a\mp ba(b+c)=ab+ac

-(-a)=a

## Fractions Rules

\frac{0}{a}=0 \: ,\: a\ne 0\frac{a}{1}=a

\frac{a}{a}=1(\frac{a}{b})^{-1}=\frac{1}{\frac{a}{b}}=\frac{b}{a}

(\frac{a}{b})^{-c}=((\frac{a}{b})^{-1})^{c}=(\frac{b}{a})^{c}a^{-1}=\frac{1}{a}

a^{-b}=\frac{1}{a^b}\frac{-a}{-b}=\frac{a}{b}

\frac{-a}{b}=-\frac{a}{b}\frac{a}{-b}=-\frac{a}{b}

\frac{a}{\frac{b}{c}}=\frac{a\cdot articling agrologist method ontario essay \cdot a}

\frac{1}{\frac{b}{c}}=\frac{c}{b}

## Absolute Rules

\left|-a\right|=a\left|a\right|=a \: ,\: a\ge0

\left| -a \right| = \left| a good \right| \left| ax\right| = some sort of \left| x\right| \:\: a\ge 0

## Exponent Rules

1^{a}=1a^{1}=a

a^{0}=1\:,\: a\ne 00^{a}=0\:,\: a\ne 0

(ab)^n=a^{n}b^{n}\frac{a^m}{a^n}=a^{m-n}\:,\: m>n

\frac{a^m}{a^n}=\frac{1}{a^{n-m}}\:,\: n>ma^{b+c}=a^{b}a^{c}

(a^{b})^{c}=a^{b\cdot c}a^{bx}=(a^b)^x

(\frac{a}{b})^{c}=\frac{a^{c}}{b^{c}}a^c \cdot b^c=(a\cdot b)^{c}

\sqrt{1}=1\sqrt{0}=0

\sqrt[n]{a}=a^{\frac{1}{n}}\sqrt[n]{a^m}=a^{\frac{m}{n}}

\sqrt{a}\sqrt{a}=a\sqrt[n]{a^n}=a,\:a\ge0

\sqrt[n]{a^n}=|a|,\:\mathrm{n\:is\:even}\sqrt[n]{a^n}=a,\:\mathrm{n\:is\:odd}

\sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b},\:a,b\ge0\sqrt[n]{\frac{a}{b}}=\frac{\sqrt[n]{a}}{\sqrt[n]{b}},\:a,b\ge0

## Factorial Rules

\frac{n!}{(n+m)!}=\frac{1}{(n+1)\cdot(n+2)\cdots(n+m)}\frac{n!}{(n-m)!}=n\cdot(n-1)\cdots(n-m+1), n>m

0!=1n!=1\cdot2\cdots(n-2)\cdot(n-1)\cdot n

## Log Rules

\log(0)=-\infty\log(1)=0

\log_a(a)=1\log_{a}(x^b)=b\cdot\log_{a}(x)

\log_{a^b}(x)=\frac{1}{b}\log_{a}(x)\log_{a}(\frac{1}{x})=-\log_{a}(x)

\log_{\frac{1}{a}}(x)=-\log_{a}(x)\log_{x^n}(x)=\frac{1}{n}

\log_{a}(b)=\frac{\ln(b)}{\ln(a)}\log_{x}(x^n)=n

\log_{x}((\frac{1}{x})^{n})=-na^{\log_{a}(b)}=b

## Undefined

0^{0}=\mathrm{Undefined}\frac{x}{0}=\mathrm{Undefined}

\log_{a}(b)=\mathrm{Undefined}\:,\: a\le0\log_{a}(b)=\mathrm{Undefined}\:,\: b\le0

\log_{1}(a)=\mathrm{Undefined}

## Complex Number Rules

i^{2}=-1\sqrt{-1}=i

\sqrt{-a}=\sqrt{-1}\sqrt{a}

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