lehrkraefte:blc:miniaufgaben:kw08-2022 [https://fginfo.ksbg.ch Fachgruppe Informatik der KSBG]

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<PRELOAD>
  miniaufgabe.js
</PRELOAD>




==== 21. Februar 2022 bis 25. Februar 2022 ====
=== Donnerstag 24. Februar 2022 ===
Faktorisieren<JS>miniAufgabe("#exofaktorisieren1","#solfaktorisieren1",
[["$\\displaystyle 147c^{4}d^{3}+168c^{3}d^{4}+48c^{2}d^{5}$", "$\\displaystyle 3c^{2}d^{3} \\cdot \\left(49c^{2}+56cd+16d^{2}\\right) = 3c^{2}d^{3} \\cdot \\left(4d+7c\\right)^2$"], ["$\\displaystyle 441a^{3}p^{2}+756a^{2}p^{3}+324ap^{4}$", "$\\displaystyle 9ap^{2} \\cdot \\left(49a^{2}+84ap+36p^{2}\\right) = 9ap^{2} \\cdot \\left(7a+6p\\right)^2$"], ["$\\displaystyle 576e^{5}u^{3}+1008e^{4}u^{4}+441e^{3}u^{5}$", "$\\displaystyle 9e^{3}u^{3} \\cdot \\left(64e^{2}+112eu+49u^{2}\\right) = 9e^{3}u^{3} \\cdot \\left(7u+8e\\right)^2$"], ["$\\displaystyle 243p^{6}y+216p^{4}y^{2}+48p^{2}y^{3}$", "$\\displaystyle 3p^{2}y \\cdot \\left(81p^{4}+72p^{2}y+16y^{2}\\right) = 3p^{2}y \\cdot \\left(9p^{2}+4y\\right)^2$"], ["$\\displaystyle 384a^{5}f^{3}+672a^{4}f^{4}+294a^{3}f^{5}$", "$\\displaystyle 6a^{3}f^{3} \\cdot \\left(64a^{2}+112af+49f^{2}\\right) = 6a^{3}f^{3} \\cdot \\left(8a+7f\\right)^2$"], ["$\\displaystyle 486a^{4}k^{3}+432a^{3}k^{4}+96a^{2}k^{5}$", "$\\displaystyle 6a^{2}k^{3} \\cdot \\left(81a^{2}+72ak+16k^{2}\\right) = 6a^{2}k^{3} \\cdot \\left(4k+9a\\right)^2$"], ["$\\displaystyle 243k^{4}u^{3}+378k^{3}u^{4}+147k^{2}u^{5}$", "$\\displaystyle 3k^{2}u^{3} \\cdot \\left(81k^{2}+126ku+49u^{2}\\right) = 3k^{2}u^{3} \\cdot \\left(9k+7u\\right)^2$"], ["$\\displaystyle 294n^{6}s+252n^{4}s^{2}+54n^{2}s^{3}$", "$\\displaystyle 6n^{2}s \\cdot \\left(49n^{4}+42n^{2}s+9s^{2}\\right) = 6n^{2}s \\cdot \\left(3s+7n^{2}\\right)^2$"], ["$\\displaystyle 648k^{6}n+1008k^{4}n^{3}+392k^{2}n^{5}$", "$\\displaystyle 8k^{2}n \\cdot \\left(81k^{4}+126k^{2}n^{2}+49n^{4}\\right) = 8k^{2}n \\cdot \\left(7n^{2}+9k^{2}\\right)^2$"], ["$\\displaystyle 486d^{6}e^{2}+864d^{4}e^{3}+384d^{2}e^{4}$", "$\\displaystyle 6d^{2}e^{2} \\cdot \\left(81d^{4}+144d^{2}e+64e^{2}\\right) = 6d^{2}e^{2} \\cdot \\left(9d^{2}+8e\\right)^2$"]],
" <hr> ", " <hr> ");
</JS>
<HTML>
<div id="exofaktorisieren1"></div>

</HTML>
<hidden Lösungen>
<HTML>
<div id="solfaktorisieren1"></div>
<div style='font-size:12px;color:gray;'>ruby faktorisieren.rb 1</div>
</HTML>

</hidden>

=== Freitag 25. Februar 2022 ===
Ausmultiplizieren und Zusammenfassen<JS>miniAufgabe("#exoausmult1","#solausmult1",
[["$\\displaystyle \\left(3a^{3}+4w^{3}\\right)\\cdot\\left(3a^{3}-5h^{2}\\right)-\\left(3a^{3}-4w^{3}\\right)\\cdot\\left(-3a^{3}-5h^{2}\\right)$", "$\\displaystyle 9a^{6}-15a^{3}h^{2}+12a^{3}w^{3}-20h^{2}w^{3} - \\left(-9a^{6}-15a^{3}h^{2}+12a^{3}w^{3}+20h^{2}w^{3}\\right) = 9a^{6}-15a^{3}h^{2}+12a^{3}w^{3}-20h^{2}w^{3} +9a^{6}+15a^{3}h^{2}-12a^{3}w^{3}-20h^{2}w^{3} = 18a^{6}-40h^{2}w^{3}$"], ["$\\displaystyle \\left(4c^{3}+5u^{3}\\right)\\cdot\\left(3n^{2}+5u^{3}\\right)-\\left(4c^{3}-5u^{3}\\right)\\cdot\\left(3n^{2}-5u^{3}\\right)$", "$\\displaystyle 12c^{3}n^{2}+20c^{3}u^{3}+15n^{2}u^{3}+25u^{6} - \\left(12c^{3}n^{2}-20c^{3}u^{3}-15n^{2}u^{3}+25u^{6}\\right) = 12c^{3}n^{2}+20c^{3}u^{3}+15n^{2}u^{3}+25u^{6} -12c^{3}n^{2}+20c^{3}u^{3}+15n^{2}u^{3}-25u^{6} = 40c^{3}u^{3}+30n^{2}u^{3}$"], ["$\\displaystyle \\left(5f^{3}+3s^{2}\\right)\\cdot\\left(-4p^{3}+3s^{2}\\right)-\\left(-5f^{3}+3s^{2}\\right)\\cdot\\left(-4p^{3}-3s^{2}\\right)$", "$\\displaystyle -20f^{3}p^{3}+15f^{3}s^{2}-12p^{3}s^{2}+9s^{4} - \\left(20f^{3}p^{3}+15f^{3}s^{2}-12p^{3}s^{2}-9s^{4}\\right) = -20f^{3}p^{3}+15f^{3}s^{2}-12p^{3}s^{2}+9s^{4} -20f^{3}p^{3}-15f^{3}s^{2}+12p^{3}s^{2}+9s^{4} = -40f^{3}p^{3}+18s^{4}$"], ["$\\displaystyle \\left(5m^{2}+3n^{3}\\right)\\cdot\\left(-4a^{2}+3n^{3}\\right)-\\left(5m^{2}-3n^{3}\\right)\\cdot\\left(4a^{2}+3n^{3}\\right)$", "$\\displaystyle -20a^{2}m^{2}-12a^{2}n^{3}+15m^{2}n^{3}+9n^{6} - \\left(20a^{2}m^{2}-12a^{2}n^{3}+15m^{2}n^{3}-9n^{6}\\right) = -20a^{2}m^{2}-12a^{2}n^{3}+15m^{2}n^{3}+9n^{6} -20a^{2}m^{2}+12a^{2}n^{3}-15m^{2}n^{3}+9n^{6} = -40a^{2}m^{2}+18n^{6}$"], ["$\\displaystyle \\left(5f^{3}+3h^{2}\\right)\\cdot\\left(4e^{2}+5f^{3}\\right)-\\left(5f^{3}-3h^{2}\\right)\\cdot\\left(4e^{2}-5f^{3}\\right)$", "$\\displaystyle 20e^{2}f^{3}+12e^{2}h^{2}+25f^{6}+15f^{3}h^{2} - \\left(20e^{2}f^{3}-12e^{2}h^{2}-25f^{6}+15f^{3}h^{2}\\right) = 20e^{2}f^{3}+12e^{2}h^{2}+25f^{6}+15f^{3}h^{2} -20e^{2}f^{3}+12e^{2}h^{2}+25f^{6}-15f^{3}h^{2} = 24e^{2}h^{2}+50f^{6}$"], ["$\\displaystyle \\left(5e^{2}+3x^{3}\\right)\\cdot\\left(4w^{3}+3x^{3}\\right)-\\left(5e^{2}-3x^{3}\\right)\\cdot\\left(-4w^{3}+3x^{3}\\right)$", "$\\displaystyle 20e^{2}w^{3}+15e^{2}x^{3}+12w^{3}x^{3}+9x^{6} - \\left(-20e^{2}w^{3}+15e^{2}x^{3}+12w^{3}x^{3}-9x^{6}\\right) = 20e^{2}w^{3}+15e^{2}x^{3}+12w^{3}x^{3}+9x^{6} +20e^{2}w^{3}-15e^{2}x^{3}-12w^{3}x^{3}+9x^{6} = 40e^{2}w^{3}+18x^{6}$"], ["$\\displaystyle \\left(3u^{2}+4x^{3}\\right)\\cdot\\left(5c^{3}+3u^{2}\\right)-\\left(-3u^{2}+4x^{3}\\right)\\cdot\\left(-5c^{3}+3u^{2}\\right)$", "$\\displaystyle 15c^{3}u^{2}+20c^{3}x^{3}+9u^{4}+12u^{2}x^{3} - \\left(15c^{3}u^{2}-20c^{3}x^{3}-9u^{4}+12u^{2}x^{3}\\right) = 15c^{3}u^{2}+20c^{3}x^{3}+9u^{4}+12u^{2}x^{3} -15c^{3}u^{2}+20c^{3}x^{3}+9u^{4}-12u^{2}x^{3} = 40c^{3}x^{3}+18u^{4}$"], ["$\\displaystyle \\left(4s^{2}-3x^{3}\\right)\\cdot\\left(4s^{2}-5u^{2}\\right)-\\left(-4s^{2}-3x^{3}\\right)\\cdot\\left(4s^{2}+5u^{2}\\right)$", "$\\displaystyle 16s^{4}-20s^{2}u^{2}-12s^{2}x^{3}+15u^{2}x^{3} - \\left(-16s^{4}-20s^{2}u^{2}-12s^{2}x^{3}-15u^{2}x^{3}\\right) = 16s^{4}-20s^{2}u^{2}-12s^{2}x^{3}+15u^{2}x^{3} +16s^{4}+20s^{2}u^{2}+12s^{2}x^{3}+15u^{2}x^{3} = 32s^{4}+30u^{2}x^{3}$"], ["$\\displaystyle \\left(3m^{2}+4u^{3}\\right)\\cdot\\left(4u^{3}+5y^{2}\\right)-\\left(-3m^{2}+4u^{3}\\right)\\cdot\\left(4u^{3}-5y^{2}\\right)$", "$\\displaystyle 12m^{2}u^{3}+15m^{2}y^{2}+16u^{6}+20u^{3}y^{2} - \\left(-12m^{2}u^{3}+15m^{2}y^{2}+16u^{6}-20u^{3}y^{2}\\right) = 12m^{2}u^{3}+15m^{2}y^{2}+16u^{6}+20u^{3}y^{2} +12m^{2}u^{3}-15m^{2}y^{2}-16u^{6}+20u^{3}y^{2} = 24m^{2}u^{3}+40u^{3}y^{2}$"], ["$\\displaystyle \\left(-4f^{2}+3n^{3}\\right)\\cdot\\left(3n^{3}-5p^{2}\\right)-\\left(4f^{2}+3n^{3}\\right)\\cdot\\left(3n^{3}+5p^{2}\\right)$", "$\\displaystyle -12f^{2}n^{3}+20f^{2}p^{2}+9n^{6}-15n^{3}p^{2} - \\left(12f^{2}n^{3}+20f^{2}p^{2}+9n^{6}+15n^{3}p^{2}\\right) = -12f^{2}n^{3}+20f^{2}p^{2}+9n^{6}-15n^{3}p^{2} -12f^{2}n^{3}-20f^{2}p^{2}-9n^{6}-15n^{3}p^{2} = -24f^{2}n^{3}-30n^{3}p^{2}$"]],
" <hr> ", " <hr> ");
</JS>
<HTML>
<div id="exoausmult1"></div>

</HTML>
<hidden Lösungen>
<HTML>
<div id="solausmult1"></div>
<div style='font-size:12px;color:gray;'>ruby ausmultiplizieren2.rb 1</div>
</HTML>

</hidden>