Algebraic Formulas

Página 1

Quadratic Formula

\begin{array}{*{20}c}

{x = \frac{{ - b \pm \sqrt {b^2 - 4ac} }}{{2a}}} & {{\rm{when}}} & {ax^2 + bx + c = 0} \\

\end{array}

Laws of Exponents

\[\ (x^m)(x^n) = x^{m+n} \] Ex.\[\ (2^2)(2^3) = 2^{2+3}=2^5 = 32 \]

\[\ (xy)^m = (x^m)(y^m) \] Ex. \[\ (2*3)² = 2²*3² = 36 \]

\[\ (x^m)^n = x^{mn} \] Ex. \[\ (2^2)^3 = 2^{2*3} = 64 \]

\[\ x^0 = 1 \] Ex. \[\ 5^0 = 1 \]

\[\frac {x^m}{x^n} = x^m-n \] Ex. \[\frac {x^5}{x^3} = x^{5-3} = x^2 \]

\[\ x^m + y^n = cannot\:be\:simplified \] Ex. \[\ x^2 + y^3 = cannot\:be\:simplified \]

Binomial Theorem

\begin{array}{*{20}c} (x+y)^1 = x + y \\ \end{array}

\begin{array}{*{20}c} (x+y)^2 = x^2 + 2xy + y^2 \\ \end{array}

\begin{array}{*{20}c} (x+y)^3 = x^3 + 3x^2y + 3xy^2 + y^3 \\ \end{array}

\begin{array}{*{20}c} (x+y)^4= x^4 + 4x^3y^2 + 6x^2y^2 + 4xy^3 + y^4 \\ \end{array}

\begin{array}{*{20}c} (x+y)^5= x^5 + 5x^4y + 10x^3y^2 + 10x^2y^3 + 5xy^4 +y^5 \\ \end{array}

Rules of 0

\[\ \frac {0}{x} = 0\;{\rm where\:x\:is\:not\:equal\:to}\:0 \]

\[\ 0^x = 0 \]

\[\ \frac {x}{0} ={\rm undefined,\:you\:can't\:do\:it} \]