lehrkraefte:blc:miniaufgaben:kw09-2026 [https://fginfo.ksbg.ch Fachgruppe Informatik der KSBG]

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<PRELOAD>
  miniaufgabe.js
</PRELOAD>



==== Montag 2. März 2026 ====
=== Aufgabe 1 ===
Binomische Formeln anwenden, Resultat in Normalform<JS>miniAufgabe("#exobinomischeFormeln1","#solbinomischeFormeln1",
[["a) $\\displaystyle \\left(3a^{2}k^{3}+2a^{3}w\\right)^2$ $\\quad$b) $\\displaystyle \\left(5d^{3}p^{2}-4d^{2}y^{2}\\right)^2$ $\\quad$c) $\\displaystyle \\left(2a^{3}x^{2}+3p^{2}x^{2}\\right)\\cdot \\left(2a^{3}x^{2}-3p^{2}x^{2}\\right)$ $\\quad$", "a) $\\displaystyle 9a^{4}k^{6}+12a^{5}k^{3}w+4a^{6}w^{2}$<br>\nb) $\\displaystyle 25d^{6}p^{4}-40d^{5}p^{2}y^{2}+16d^{4}y^{4}$<br>\nc) $\\displaystyle 4a^{6}x^{4}-9p^{4}x^{4}$<br>\n"], ["a) $\\displaystyle \\left(3c^{3}n^{3}+5n^{3}w^{3}\\right)^2$ $\\quad$b) $\\displaystyle \\left(5m^{3}y^{2}-7h^{2}y\\right)^2$ $\\quad$c) $\\displaystyle \\left(6x^{3}y^{3}+4nx\\right)\\cdot \\left(6x^{3}y^{3}-4nx\\right)$ $\\quad$", "a) $\\displaystyle 9c^{6}n^{6}+30c^{3}n^{6}w^{3}+25n^{6}w^{6}$<br>\nb) $\\displaystyle 25m^{6}y^{4}-70h^{2}m^{3}y^{3}+49h^{4}y^{2}$<br>\nc) $\\displaystyle 36x^{6}y^{6}-16n^{2}x^{2}$<br>\n"], ["a) $\\displaystyle \\left(7af^{3}+2am\\right)^2$ $\\quad$b) $\\displaystyle \\left(2h^{2}m^{3}-6e^{2}h\\right)^2$ $\\quad$c) $\\displaystyle \\left(6k^{3}p+5kx\\right)\\cdot \\left(6k^{3}p-5kx\\right)$ $\\quad$", "a) $\\displaystyle 49a^{2}f^{6}+28a^{2}f^{3}m+4a^{2}m^{2}$<br>\nb) $\\displaystyle 4h^{4}m^{6}-24e^{2}h^{3}m^{3}+36e^{4}h^{2}$<br>\nc) $\\displaystyle 36k^{6}p^{2}-25k^{2}x^{2}$<br>\n"], ["a) $\\displaystyle \\left(5k^{3}w^{2}+6p^{3}w\\right)^2$ $\\quad$b) $\\displaystyle \\left(2f^{3}n^{2}-5hn\\right)^2$ $\\quad$c) $\\displaystyle \\left(4hn^{3}+5hw^{3}\\right)\\cdot \\left(4hn^{3}-5hw^{3}\\right)$ $\\quad$", "a) $\\displaystyle 25k^{6}w^{4}+60k^{3}p^{3}w^{3}+36p^{6}w^{2}$<br>\nb) $\\displaystyle 4f^{6}n^{4}-20f^{3}hn^{3}+25h^{2}n^{2}$<br>\nc) $\\displaystyle 16h^{2}n^{6}-25h^{2}w^{6}$<br>\n"], ["a) $\\displaystyle \\left(7c^{3}e+3e^{2}x\\right)^2$ $\\quad$b) $\\displaystyle \\left(3k^{2}p^{2}-7n^{2}p\\right)^2$ $\\quad$c) $\\displaystyle \\left(2m^{3}y^{3}+7k^{2}y^{2}\\right)\\cdot \\left(2m^{3}y^{3}-7k^{2}y^{2}\\right)$ $\\quad$", "a) $\\displaystyle 49c^{6}e^{2}+42c^{3}e^{3}x+9e^{4}x^{2}$<br>\nb) $\\displaystyle 9k^{4}p^{4}-42k^{2}n^{2}p^{3}+49n^{4}p^{2}$<br>\nc) $\\displaystyle 4m^{6}y^{6}-49k^{4}y^{4}$<br>\n"], ["a) $\\displaystyle \\left(5a^{2}e^{3}+3e^{2}h^{2}\\right)^2$ $\\quad$b) $\\displaystyle \\left(2c^{3}n^{3}-3ck^{2}\\right)^2$ $\\quad$c) $\\displaystyle \\left(6kn^{3}+5k^{2}w\\right)\\cdot \\left(6kn^{3}-5k^{2}w\\right)$ $\\quad$", "a) $\\displaystyle 25a^{4}e^{6}+30a^{2}e^{5}h^{2}+9e^{4}h^{4}$<br>\nb) $\\displaystyle 4c^{6}n^{6}-12c^{4}k^{2}n^{3}+9c^{2}k^{4}$<br>\nc) $\\displaystyle 36k^{2}n^{6}-25k^{4}w^{2}$<br>\n"], ["a) $\\displaystyle \\left(3d^{3}k^{2}+7fk\\right)^2$ $\\quad$b) $\\displaystyle \\left(2ep^{2}-6cp\\right)^2$ $\\quad$c) $\\displaystyle \\left(2d^{3}w^{3}+5h^{3}w^{2}\\right)\\cdot \\left(2d^{3}w^{3}-5h^{3}w^{2}\\right)$ $\\quad$", "a) $\\displaystyle 9d^{6}k^{4}+42d^{3}fk^{3}+49f^{2}k^{2}$<br>\nb) $\\displaystyle 4e^{2}p^{4}-24cep^{3}+36c^{2}p^{2}$<br>\nc) $\\displaystyle 4d^{6}w^{6}-25h^{6}w^{4}$<br>\n"], ["a) $\\displaystyle \\left(4f^{2}m^{3}+6m^{2}y^{2}\\right)^2$ $\\quad$b) $\\displaystyle \\left(5a^{2}d^{3}-4d^{2}x^{2}\\right)^2$ $\\quad$c) $\\displaystyle \\left(6e^{2}k^{3}+7kn^{3}\\right)\\cdot \\left(6e^{2}k^{3}-7kn^{3}\\right)$ $\\quad$", "a) $\\displaystyle 16f^{4}m^{6}+48f^{2}m^{5}y^{2}+36m^{4}y^{4}$<br>\nb) $\\displaystyle 25a^{4}d^{6}-40a^{2}d^{5}x^{2}+16d^{4}x^{4}$<br>\nc) $\\displaystyle 36e^{4}k^{6}-49k^{2}n^{6}$<br>\n"], ["a) $\\displaystyle \\left(4f^{3}y^{3}+7ey^{2}\\right)^2$ $\\quad$b) $\\displaystyle \\left(7c^{2}e^{3}-2c^{2}k\\right)^2$ $\\quad$c) $\\displaystyle \\left(6a^{2}h^{2}+7a^{2}f\\right)\\cdot \\left(6a^{2}h^{2}-7a^{2}f\\right)$ $\\quad$", "a) $\\displaystyle 16f^{6}y^{6}+56ef^{3}y^{5}+49e^{2}y^{4}$<br>\nb) $\\displaystyle 49c^{4}e^{6}-28c^{4}e^{3}k+4c^{4}k^{2}$<br>\nc) $\\displaystyle 36a^{4}h^{4}-49a^{4}f^{2}$<br>\n"], ["a) $\\displaystyle \\left(7n^{3}x^{3}+3kx^{2}\\right)^2$ $\\quad$b) $\\displaystyle \\left(5c^{2}h-4ck\\right)^2$ $\\quad$c) $\\displaystyle \\left(2f^{3}y^{3}+6k^{2}y^{3}\\right)\\cdot \\left(2f^{3}y^{3}-6k^{2}y^{3}\\right)$ $\\quad$", "a) $\\displaystyle 49n^{6}x^{6}+42kn^{3}x^{5}+9k^{2}x^{4}$<br>\nb) $\\displaystyle 25c^{4}h^{2}-40c^{3}hk+16c^{2}k^{2}$<br>\nc) $\\displaystyle 4f^{6}y^{6}-36k^{4}y^{6}$<br>\n"]],
" <hr> ", " <hr> ");
</JS>
<HTML>
<div id="exobinomischeFormeln1"></div>

</HTML>
<hidden Lösungen>

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<div id="solbinomischeFormeln1"></div>
<div style='font-size:12px;color:gray;'>ruby ausmultiplizieren2.rb 4</div>
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</hidden>
=== Aufgabe 2 ===
Gemeinsame Faktoren ausklammern, dann die Klammer mit binomischen Formeln faktorisieren.

<JS>miniAufgabe("#exofaktorisierenMitBinom","#solfaktorisierenMitBinom",
[['$\\displaystyle 75d^{2}k^{6}n+90d^{2}k^{3}n^{4}+27d^{2}n^{7}$', '$\\displaystyle 75d^{2}k^{6}n+90d^{2}k^{3}n^{4}+27d^{2}n^{7} = 3d^{2}n \\cdot \\left(25k^{6}+30k^{3}n^{3}+9n^{6}\\right) = 3d^{2}n \\cdot \\left(3n^{3}+5k^{3}\\right)^{2}$'], ['$\\displaystyle 8a^{6}k^{3}m-40a^{3}k^{3}m^{3}+50k^{3}m^{5}$', '$\\displaystyle 8a^{6}k^{3}m-40a^{3}k^{3}m^{3}+50k^{3}m^{5} = 2k^{3}m \\cdot \\left(4a^{6}-20a^{3}m^{2}+25m^{4}\\right) = 2k^{3}m \\cdot \\left(2a^{3}-5m^{2}\\right)^{2}$'], ['$\\displaystyle 64e^{3}p^{7}-36e^{3}k^{4}p$', '$\\displaystyle 64e^{3}p^{7}-36e^{3}k^{4}p = 4e^{3}p \\cdot \\left(16p^{6}-9k^{4}\\right) = 4e^{3}p \\cdot \\left(4p^{3}+3k^{2}\\right) \\cdot \\left(4p^{3}-3k^{2}\\right)$'], ['$\\displaystyle 18h^{6}pw^{3}+24h^{3}p^{4}w^{3}+8p^{7}w^{3}$', '$\\displaystyle 18h^{6}pw^{3}+24h^{3}p^{4}w^{3}+8p^{7}w^{3} = 2w^{3}p \\cdot \\left(9h^{6}+12h^{3}p^{3}+4p^{6}\\right) = 2w^{3}p \\cdot \\left(2p^{3}+3h^{3}\\right)^{2}$'], ['$\\displaystyle 80dn^{6}p^{2}-200d^{3}n^{3}p^{2}+125d^{5}p^{2}$', '$\\displaystyle 80dn^{6}p^{2}-200d^{3}n^{3}p^{2}+125d^{5}p^{2} = 5p^{2}d \\cdot \\left(16n^{6}-40d^{2}n^{3}+25d^{4}\\right) = 5p^{2}d \\cdot \\left(4n^{3}-5d^{2}\\right)^{2}$'], ['$\\displaystyle 48f^{3}m^{7}-75c^{4}f^{3}m$', '$\\displaystyle 48f^{3}m^{7}-75c^{4}f^{3}m = 3f^{3}m \\cdot \\left(16m^{6}-25c^{4}\\right) = 3f^{3}m \\cdot \\left(4m^{3}+5c^{2}\\right) \\cdot \\left(4m^{3}-5c^{2}\\right)$'], ['$\\displaystyle 50e^{7}x^{2}+40e^{4}p^{3}x^{2}+8ep^{6}x^{2}$', '$\\displaystyle 50e^{7}x^{2}+40e^{4}p^{3}x^{2}+8ep^{6}x^{2} = 2x^{2}e \\cdot \\left(25e^{6}+20e^{3}p^{3}+4p^{6}\\right) = 2x^{2}e \\cdot \\left(5e^{3}+2p^{3}\\right)^{2}$'], ['$\\displaystyle 80a^{5}x^{3}-120a^{3}e^{2}x^{3}+45ae^{4}x^{3}$', '$\\displaystyle 80a^{5}x^{3}-120a^{3}e^{2}x^{3}+45ae^{4}x^{3} = 5x^{3}a \\cdot \\left(16a^{4}-24a^{2}e^{2}+9e^{4}\\right) = 5x^{3}a \\cdot \\left(3e^{2}-4a^{2}\\right)^{2}$'], ['$\\displaystyle 16d^{2}fx^{6}-36d^{2}f^{5}$', '$\\displaystyle 16d^{2}fx^{6}-36d^{2}f^{5} = 4d^{2}f \\cdot \\left(4x^{6}-9f^{4}\\right) = 4d^{2}f \\cdot \\left(2x^{3}+3f^{2}\\right) \\cdot \\left(2x^{3}-3f^{2}\\right)$'], ['$\\displaystyle 32m^{2}w^{5}+80m^{2}w^{3}x^{2}+50m^{2}wx^{4}$', '$\\displaystyle 32m^{2}w^{5}+80m^{2}w^{3}x^{2}+50m^{2}wx^{4} = 2m^{2}w \\cdot \\left(16w^{4}+40w^{2}x^{2}+25x^{4}\\right) = 2m^{2}w \\cdot \\left(5x^{2}+4w^{2}\\right)^{2}$'], ['$\\displaystyle 27e^{6}p^{3}w-36e^{3}p^{3}w^{4}+12p^{3}w^{7}$', '$\\displaystyle 27e^{6}p^{3}w-36e^{3}p^{3}w^{4}+12p^{3}w^{7} = 3p^{3}w \\cdot \\left(9e^{6}-12e^{3}w^{3}+4w^{6}\\right) = 3p^{3}w \\cdot \\left(2w^{3}-3e^{3}\\right)^{2}$'], ['$\\displaystyle 18ef^{2}y^{6}-8e^{5}f^{2}$', '$\\displaystyle 18ef^{2}y^{6}-8e^{5}f^{2} = 2f^{2}e \\cdot \\left(9y^{6}-4e^{4}\\right) = 2f^{2}e \\cdot \\left(3y^{3}+2e^{2}\\right) \\cdot \\left(3y^{3}-2e^{2}\\right)$']],
' <hr> ', ' <hr> ');
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<div id="exofaktorisierenMitBinom"></div>

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<hidden Lösungen>

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<div id="solfaktorisierenMitBinom"></div>
<div style='font-size:12px;color:gray;'>python /home/ivo/burggraben/git/ivo/math/miniaufgaben/headerfooter.py faktorisieren-mit-binomen.py</div>
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