Faktorisasi - Clavius

Faktorisasi Kuadrat

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

Faktorisasi Kubik

\(a^3 - b^3 = (a - b)(a^2 + ab + b^2)\)

\(a^3 + b^3 = (a + b)(a^2 - ab + b^2)\)

Contoh 01

Faktorkan \(9b^2 - 400\)

\begin{equation*} \begin{split} & (3b)^2 - 20^2 \\\\ & (3b + 20)(3b - 20) \end{split} \end{equation*}

Contoh 02

Jabarkan \((4x + 5)(4x - 5)\)

\begin{equation*} \begin{split} & (4x)^2 - 5^2\\\\ & 16x^2 - 25 \end{split} \end{equation*}

Contoh 03

Faktorkan \(x^3 + 8\)

\begin{equation*} \begin{split} & x^3 + 8 \\\\ & x^3 + 2^3\\\\ & (x + 2)(x^2 + 2x + 4) \end{split} \end{equation*}

Contoh 04

Faktorkan \(125x^3 - 27y^3\)

\begin{equation*} \begin{split} & 125x^3 - 27y^3 \\\\ & (5x)^3 - (3y)^3\\\\ & (5x -3 y)(25x^2 + 15xy + 9y^2) \end{split} \end{equation*}