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12.3: Important and Useful Rules/Formulas

  • Page ID
    49419
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    Exponents (Assume each expression is defined.)

    \(a^na^m = a^{n + m}\)

    \(\dfrac{a^n}{a^m} = a^{n - m}\)

    \((a^n)^m = a^{nm}\)

    \((ab)^n = a^nb^n\)

    \(a^{-1} = \dfrac{1}{n}\)

    \(a^{-n} = \dfrac{1}{a^n}\)

    \(a^0 = 1\)

    \((\dfrac{a}{b})^n = \dfrac{a^n}{b^n}\)

    Factorization and special product formulas

    \(ab + ac = a(b + c)\)

    \(a^2 + 2a +b^2 = (a+b)^2\)

    \(a^2 - b^2 = (a + b)(a - b)\)

    \(a^2 - 2ab + b^2 = (a-b)^2\)

    Formulas

    \(\begin{array}{flushleft}
    x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} & \text{ Quadratic formula}\\
    y = mx + b & \text{ Slope-intercept form of a straight line}\\
    y - y_1 = m(x - x_1) & \text{ Point-slope form of a straight line}\\
    m = \dfrac{y_2 - y_1}{x_2 - x_1} & \text{ Slope of a straight line passing through the points } (x_1, x_2) \text{ and } (y_1, y_2)
    \end{array}\)


    This page titled 12.3: Important and Useful Rules/Formulas is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Denny Burzynski & Wade Ellis, Jr. (OpenStax CNX) .

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