We've updated our
Privacy Policy effective December 15. Please read our updated Privacy Policy and tap

TEXT

Álgebra Folha de Apoio

Folhas de dicas de matemática da Symbolab


Álgebra Folha de Apoio

Regras de Número

a\cdot 0=0 1\cdot a=a


Regras de Expansão

-(a\pm b)=-a\mp b a(b+c)=ab+ac
a(b+c)(d+e)=abd+abe+acd+ace (a+b)(c+d)=ac+ad+bc+bd
-(-a)=a


Regras de Frações

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


Regras de Absoluto

\left| -a \right| = \left| a \right| \left|a\right|=a \: ,\: a\ge0
\left| ax\right| = a \left| x\right| \: , \: a\ge 0


Regras de Expoente

1^{a}=1 a^{1}=a
a^{0}=1\:,\: a\ne 0 0^{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>m a^{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}


Regras radicais

\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\:é\:par} \sqrt[n]{a^n}=a,\:\mathrm{n\:é\:ímpar}
\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


Regras de Fator

x^{2}-y^{2} = (x-y)(x+y)
x^{3}+y^{3} = (x+y)(x^{2}-xy+ y^{2})
x^{n}-y^{n} = (x-y)(x^{n-1}+x^{n-2}y+ \dots + xy^{n-2} + y^{n-1})
x^{n}+y^{n} = (x+y)(x^{n-1}-x^{n-2}y+ \dots - xy^{n-2} + y^{n-1}) \quad \quad \mathrm{n\:é\:ímpar}
ax^(2n)-b = (\sqrt{a}x^n+\sqrt{b})(\sqrt{a}x^n-\sqrt{b})
ax^(4)-b = (\sqrt{a}x^2+\sqrt{b})(\sqrt{a}x^2-\sqrt{b})
ax^(2n)-by^(2m) = (\sqrt{a}x^n+\sqrt{b}y^m)(\sqrt{a}x^n-\sqrt{b}y^m)
ax^(4)-by^(4) = (\sqrt{a}x^2+\sqrt{b}y^2)(\sqrt{a}x^2-\sqrt{b}y^2)


Regras de Fatorial

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


Regras de Log

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


Indefinido

0^{0}=\mathrm{Indefinido} \frac{x}{0}=\mathrm{Indefinido}
\log_{a}(b)=\mathrm{Indefinido}\:,\: a\le0 \log_{a}(b)=\mathrm{Indefinido}\:,\: b\le0
\log_{1}(a)=\mathrm{Indefinido}


Regras de número complexo

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