Algebra
Algebra Formulas
$-(-a)=a$$-(a + b)= -a - b$
$-(a - b)= -a + b$
$a(b+c)=ab+ac$
$a(b+c)(d+e)=abd+abe+acd+ace$
$(a+b)(c+d)=ac+ad+bc+bd$
Factor Rules
$a^{2}-b^{2} = (a-b)(a+b)$$a^{2}+b^{2} = $ - there is no such a formula.
$a^{3}-b^{3} = (a-b)(a^{2}+ab+ b^{2})$
$a^{3}+b^{3} = (a+b)(a^{2}-ab+ b^{2})$
Fraction Rules
$\frac{0}{a}=0$ a ≠ 0$\frac{a}{0}=$ the operation is undefined. Dividing by zero is not allowed.
$\frac{a}{1}=a$
$\frac{a}{a}=1$
$(\frac{a}{b})^{-1}=\frac{1}{\frac{a}{b}}=\frac{b}{a}$
$(\frac{a}{b})^{-c}=((\frac{a}{b})^{-1})^{c}=(\frac{b}{a})^{c}$
$a^{-1}=\frac{1}{a}$
$a^{-b}=\frac{1}{a^b}$
$\frac{-a}{-b}=\frac{a}{b}$
$\frac{-a}{b}=-\frac{a}{b}$
$\frac{a}{-b}=-\frac{a}{b}$
$\frac{a}{\frac{b}{c}}=\frac{a\cdot c}{b}$
$\frac{\frac{b}{c}}{a}=\frac{b}{c \cdot a}$
$\frac{1}{\frac{b}{c}}=\frac{c}{b}$
Modules
|x|=x if x ≥ 0|x|=-x if x < 0
Exponent Rules
$1^{a}=1$$a^{1}=a$
$a^{0}=1$ if a ≠ 0
$0^{a}=0$ if a ≠ 0
$(ab)^n=a^nb^n$
$\frac{a^m}{a^n}=a^{m-n}$ if m > n
$\frac{a^m}{a^n}=\frac{1}{a^{n-m}}$ if m < n
$a^{b+c}=a^{b}a^{c}$
$(a^{b})^{c}=a^{b\cdot c}$
$a^{bx}=(a^b)^x$
$(\frac{a}{b})^{c}=\frac{a^{c}}{b^{c}}$
$a^c \cdot b^c=(a\cdot b)^{c}$
$a^{\frac{m}{n}}=(\sqrt[n]{a})^{m}$
$\sqrt{-a}=\sqrt{-1}\sqrt{a}$
$\sqrt[n]{a\cdot b}=\sqrt[n]{a}\sqrt[n]{b}$
Factorial
$n!=1 \cdot 2 \cdots(n-2) \cdot (n-1) \cdot n$$0!=1$
Algebra Problem Solver
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