$f(x)=x^2+6x+8f(x)=x^\{2\}+6\; x+8$

Ergänze mit dem quadratischen Term: ${\left({\displaystyle \frac{6}{2}}\right)}^2\backslash left(\backslash dfrac\{\backslash color\{green\}6\}\{2\}\backslash right)^2$

$f(x)=\underset{1.\text{Binomische Formel}}{\underbrace{x^2+6x+{\left({\displaystyle \frac{6}{2}}\right)}^2}}+\underset{-1}{\underbrace{8-{\left({\displaystyle \frac{6}{2}}\right)}^2}}f(x)=\backslash underbrace\{x^\{2\}+6\; x+\backslash left(\backslash dfrac\{\backslash color\{green\}6\}\{2\}\backslash right)^2\}\_\{1.\; \backslash text\{Binomische\; Formel\}\}+\backslash underbrace\{8-\backslash left(\backslash dfrac\{\backslash color\{green\}6\}\{2\}\backslash right)^2\}\_\{-1\}$

Verwende nun die erste binomische Formel:

$a^2+2ab+b_{}^2=(a+b{)}^{2}a^2+2ab+b\_\{\; \}^2=(a+b)^2$

$x^2+6x+{\left({\displaystyle \frac{6}{2}}\right)}^2=(x+3{)}^{2}x^\{2\}+6\; x+\backslash left(\backslash dfrac\{\backslash color\{green\}6\}\{2\}\backslash right)^2=(x+3)^2$

Die Funktion kann dann mithilfe des Binoms geschrieben werden als:

$f(x)=(x+3{)}^2-1f(x)=(x+3)^2-1$