Algebra Formulas


$-(a + b)= -a - b$

$-(a - b)= -a + b$




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.










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

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



|x|=x     if x ≥ 0

|x|=-x     if x < 0

Exponent Rules



$a^{0}=1$     if a ≠ 0

$0^{a}=0$     if a ≠ 0


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

$\frac{a^m}{a^n}=\frac{1}{a^{n-m}}$     if m < n


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



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



$\sqrt[n]{a\cdot b}=\sqrt[n]{a}\sqrt[n]{b}$


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


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