lehrkraefte:blc:miniaufgaben:kw06-2026 [https://fginfo.ksbg.ch Fachgruppe Informatik der KSBG]

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==== Montag 9. Februar 2026 ====
Ausmultiplizieren und Zusammenfassen.<JS>miniAufgabe("#exoausmult1","#solausmult1",
[["$\\displaystyle \\left(3f^{3}+5k^{2}\\right)\\cdot\\left(-4x^{3}+5k^{2}\\right)-\\left(3f^{3}-5k^{2}\\right)\\cdot\\left(-4x^{3}-5k^{2}\\right)$", "$ \\begin{multline*}-12f^{3}x^{3}+15f^{3}k^{2}-20k^{2}x^{3}+25k^{2}k^{2} - \\left(-12f^{3}x^{3}-15f^{3}k^{2}+20k^{2}x^{3}+25k^{2}k^{2}\\right) = \\\\\n-12f^{3}x^{3}+15f^{3}k^{2}-20k^{2}x^{3}+25k^{2}k^{2} +12f^{3}x^{3}+15f^{3}k^{2}-20k^{2}x^{3}-25k^{2}k^{2} = \\\\\n 30f^{3}k^{2}-40k^{2}x^{3}\\end{multline*}\n$"], ["$\\displaystyle \\left(3w^{3}-4y^{3}\\right)\\cdot\\left(3w^{3}+5e^{2}\\right)-\\left(-3w^{3}-4y^{3}\\right)\\cdot\\left(3w^{3}-5e^{2}\\right)$", "$ \\begin{multline*}9w^{3}w^{3}-12w^{3}y^{3}+15e^{2}w^{3}-20e^{2}y^{3} - \\left(-9w^{3}w^{3}-12w^{3}y^{3}+15e^{2}w^{3}+20e^{2}y^{3}\\right) = \\\\\n9w^{3}w^{3}-12w^{3}y^{3}+15e^{2}w^{3}-20e^{2}y^{3} +9w^{3}w^{3}+12w^{3}y^{3}-15e^{2}w^{3}-20e^{2}y^{3} = \\\\\n 18w^{6}-40e^{2}y^{3}\\end{multline*}\n$"], ["$\\displaystyle \\left(3a^{3}-4b^{3}\\right)\\cdot\\left(3a^{3}+5d^{2}\\right)-\\left(3a^{3}+4b^{3}\\right)\\cdot\\left(-3a^{3}+5d^{2}\\right)$", "$ \\begin{multline*}9a^{3}a^{3}-12a^{3}b^{3}+15a^{3}d^{2}-20b^{3}d^{2} - \\left(-9a^{3}a^{3}-12a^{3}b^{3}+15a^{3}d^{2}+20b^{3}d^{2}\\right) = \\\\\n9a^{3}a^{3}-12a^{3}b^{3}+15a^{3}d^{2}-20b^{3}d^{2} +9a^{3}a^{3}+12a^{3}b^{3}-15a^{3}d^{2}-20b^{3}d^{2} = \\\\\n 18a^{6}-40b^{3}d^{2}\\end{multline*}\n$"], ["$\\displaystyle \\left(4y^{3}-5w^{2}\\right)\\cdot\\left(4y^{3}-3c^{2}\\right)-\\left(-4y^{3}-5w^{2}\\right)\\cdot\\left(-4y^{3}-3c^{2}\\right)$", "$ \\begin{multline*}16y^{3}y^{3}-12c^{2}y^{3}-20w^{2}y^{3}+15c^{2}w^{2} - \\left(16y^{3}y^{3}+12c^{2}y^{3}+20w^{2}y^{3}+15c^{2}w^{2}\\right) = \\\\\n16y^{3}y^{3}-12c^{2}y^{3}-20w^{2}y^{3}+15c^{2}w^{2} -16y^{3}y^{3}-12c^{2}y^{3}-20w^{2}y^{3}-15c^{2}w^{2} = \\\\\n -24c^{2}y^{3}-40w^{2}y^{3}\\end{multline*}\n$"], ["$\\displaystyle \\left(5y^{3}+3c^{2}\\right)\\cdot\\left(-4x^{3}+5y^{3}\\right)-\\left(-5y^{3}+3c^{2}\\right)\\cdot\\left(4x^{3}+5y^{3}\\right)$", "$ \\begin{multline*}-20x^{3}y^{3}+25y^{3}y^{3}-12c^{2}x^{3}+15c^{2}y^{3} - \\left(-20x^{3}y^{3}-25y^{3}y^{3}+12c^{2}x^{3}+15c^{2}y^{3}\\right) = \\\\\n-20x^{3}y^{3}+25y^{3}y^{3}-12c^{2}x^{3}+15c^{2}y^{3} +20x^{3}y^{3}+25y^{3}y^{3}-12c^{2}x^{3}-15c^{2}y^{3} = \\\\\n 50y^{6}-24c^{2}x^{3}\\end{multline*}\n$"], ["$\\displaystyle \\left(5m^{3}+3n^{3}\\right)\\cdot\\left(5m^{3}+4p^{2}\\right)-\\left(5m^{3}-3n^{3}\\right)\\cdot\\left(5m^{3}-4p^{2}\\right)$", "$ \\begin{multline*}25m^{3}m^{3}+15m^{3}n^{3}+20m^{3}p^{2}+12n^{3}p^{2} - \\left(25m^{3}m^{3}-15m^{3}n^{3}-20m^{3}p^{2}+12n^{3}p^{2}\\right) = \\\\\n25m^{3}m^{3}+15m^{3}n^{3}+20m^{3}p^{2}+12n^{3}p^{2} -25m^{3}m^{3}+15m^{3}n^{3}+20m^{3}p^{2}-12n^{3}p^{2} = \\\\\n 30m^{3}n^{3}+40m^{3}p^{2}\\end{multline*}\n$"], ["$\\displaystyle \\left(5h^{3}+3p^{3}\\right)\\cdot\\left(5h^{3}-4b^{2}\\right)-\\left(5h^{3}-3p^{3}\\right)\\cdot\\left(-5h^{3}-4b^{2}\\right)$", "$ \\begin{multline*}25h^{3}h^{3}+15h^{3}p^{3}-20b^{2}h^{3}-12b^{2}p^{3} - \\left(-25h^{3}h^{3}+15h^{3}p^{3}-20b^{2}h^{3}+12b^{2}p^{3}\\right) = \\\\\n25h^{3}h^{3}+15h^{3}p^{3}-20b^{2}h^{3}-12b^{2}p^{3} +25h^{3}h^{3}-15h^{3}p^{3}+20b^{2}h^{3}-12b^{2}p^{3} = \\\\\n 50h^{6}-24b^{2}p^{3}\\end{multline*}\n$"], ["$\\displaystyle \\left(3x^{3}+5n^{2}\\right)\\cdot\\left(-4f^{3}+3x^{3}\\right)-\\left(-3x^{3}+5n^{2}\\right)\\cdot\\left(4f^{3}+3x^{3}\\right)$", "$ \\begin{multline*}-12f^{3}x^{3}+9x^{3}x^{3}-20f^{3}n^{2}+15n^{2}x^{3} - \\left(-12f^{3}x^{3}-9x^{3}x^{3}+20f^{3}n^{2}+15n^{2}x^{3}\\right) = \\\\\n-12f^{3}x^{3}+9x^{3}x^{3}-20f^{3}n^{2}+15n^{2}x^{3} +12f^{3}x^{3}+9x^{3}x^{3}-20f^{3}n^{2}-15n^{2}x^{3} = \\\\\n 18x^{6}-40f^{3}n^{2}\\end{multline*}\n$"], ["$\\displaystyle \\left(-5b^{2}+4c^{2}\\right)\\cdot\\left(-3e^{3}+4c^{2}\\right)-\\left(-5b^{2}-4c^{2}\\right)\\cdot\\left(3e^{3}+4c^{2}\\right)$", "$ \\begin{multline*}15b^{2}e^{3}-12c^{2}e^{3}-20b^{2}c^{2}+16c^{2}c^{2} - \\left(-15b^{2}e^{3}-12c^{2}e^{3}-20b^{2}c^{2}-16c^{2}c^{2}\\right) = \\\\\n15b^{2}e^{3}-12c^{2}e^{3}-20b^{2}c^{2}+16c^{2}c^{2} +15b^{2}e^{3}+12c^{2}e^{3}+20b^{2}c^{2}+16c^{2}c^{2} = \\\\\n 30b^{2}e^{3}+32c^{4}\\end{multline*}\n$"], ["$\\displaystyle \\left(-4b^{3}+5h^{3}\\right)\\cdot\\left(5h^{3}+3a^{2}\\right)-\\left(-4b^{3}-5h^{3}\\right)\\cdot\\left(5h^{3}-3a^{2}\\right)$", "$ \\begin{multline*}-20b^{3}h^{3}+25h^{3}h^{3}-12a^{2}b^{3}+15a^{2}h^{3} - \\left(-20b^{3}h^{3}-25h^{3}h^{3}+12a^{2}b^{3}+15a^{2}h^{3}\\right) = \\\\\n-20b^{3}h^{3}+25h^{3}h^{3}-12a^{2}b^{3}+15a^{2}h^{3} +20b^{3}h^{3}+25h^{3}h^{3}-12a^{2}b^{3}-15a^{2}h^{3} = \\\\\n 50h^{6}-24a^{2}b^{3}\\end{multline*}\n$"]],
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<div style='font-size:12px;color:gray;'>ruby ausmultiplizieren2.rb 1</div>
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