<PRELOAD>
  miniaufgabe.js
</PRELOAD>


==== 28. Februar 2022 bis 4. März 2022 ====
=== Donnerstag 3. März 2022 ===

Lösen Sie die Gleichung nach $x$ auf.<JS>miniAufgabe("#exolinGleichMitBinom","#sollinGleichMitBinom",
[["$\\displaystyle \\left(\\frac{3}{2}x+\\frac{2}{3}\\right)^2 = \\left(\\frac{3}{2}x+\\frac{5}{3}\\right)\\left(\\frac{3}{2}x-\\frac{5}{3}\\right)$", "$\\begin{align*}\\left(\\frac{3}{2}x+\\frac{2}{3}\\right)^2 & = \\left(\\frac{3}{2}x+\\frac{5}{3}\\right)\\left(\\frac{3}{2}x-\\frac{5}{3}\\right) \\\\\n\\frac{9}{4}x^{2}+2x+\\frac{4}{9} & =  \\frac{9}{4}x^{2}-\\frac{25}{9} && |-\\frac{9}{4}x^{2}\\\\\n2x+\\frac{4}{9} & =  -\\frac{25}{9} && |-\\frac{4}{9}\\\\\n2x & =  -\\frac{29}{9} && | :2\\\\\nx & =  -\\frac{29}{18}\n\\end{align*}$"], ["$\\displaystyle \\left(\\frac{3}{4}x-\\frac{4}{3}\\right)^2 = \\left(\\frac{3}{4}x+\\frac{4}{3}\\right)\\left(\\frac{3}{4}x-\\frac{4}{3}\\right)$", "$\\begin{align*}\\left(\\frac{3}{4}x-\\frac{4}{3}\\right)^2 & = \\left(\\frac{3}{4}x+\\frac{4}{3}\\right)\\left(\\frac{3}{4}x-\\frac{4}{3}\\right) \\\\\n\\frac{9}{16}x^{2}-2x+\\frac{16}{9} & =  \\frac{9}{16}x^{2}-\\frac{16}{9} && |-\\frac{9}{16}x^{2}\\\\\n-2x+\\frac{16}{9} & =  -\\frac{16}{9} && |-\\frac{16}{9}\\\\\n-2x & =  -\\frac{32}{9} && | :-2\\\\\nx & =  \\frac{16}{9}\n\\end{align*}$"], ["$\\displaystyle \\left(\\frac{4}{3}x+\\frac{4}{5}\\right)^2 = \\left(\\frac{4}{3}x-\\frac{2}{5}\\right)\\left(\\frac{4}{3}x+\\frac{2}{5}\\right)$", "$\\begin{align*}\\left(\\frac{4}{3}x+\\frac{4}{5}\\right)^2 & = \\left(\\frac{4}{3}x-\\frac{2}{5}\\right)\\left(\\frac{4}{3}x+\\frac{2}{5}\\right) \\\\\n\\frac{16}{9}x^{2}+\\frac{32}{15}x+\\frac{16}{25} & =  \\frac{16}{9}x^{2}-\\frac{4}{25} && |-\\frac{16}{9}x^{2}\\\\\n\\frac{32}{15}x+\\frac{16}{25} & =  -\\frac{4}{25} && |-\\frac{16}{25}\\\\\n\\frac{32}{15}x & =  -\\frac{4}{5} && | :\\frac{32}{15}\\\\\nx & =  -\\frac{3}{8}\n\\end{align*}$"], ["$\\displaystyle \\left(\\frac{4}{3}x-\\frac{3}{4}\\right)^2 = \\left(\\frac{4}{3}x-\\frac{5}{4}\\right)\\left(\\frac{4}{3}x+\\frac{5}{4}\\right)$", "$\\begin{align*}\\left(\\frac{4}{3}x-\\frac{3}{4}\\right)^2 & = \\left(\\frac{4}{3}x-\\frac{5}{4}\\right)\\left(\\frac{4}{3}x+\\frac{5}{4}\\right) \\\\\n\\frac{16}{9}x^{2}-2x+\\frac{9}{16} & =  \\frac{16}{9}x^{2}-\\frac{25}{16} && |-\\frac{16}{9}x^{2}\\\\\n-2x+\\frac{9}{16} & =  -\\frac{25}{16} && |-\\frac{9}{16}\\\\\n-2x & =  -\\frac{17}{8} && | :-2\\\\\nx & =  \\frac{17}{16}\n\\end{align*}$"], ["$\\displaystyle \\left(\\frac{5}{4}x-\\frac{2}{3}\\right)^2 = \\left(\\frac{5}{4}x+\\frac{4}{3}\\right)\\left(\\frac{5}{4}x-\\frac{4}{3}\\right)$", "$\\begin{align*}\\left(\\frac{5}{4}x-\\frac{2}{3}\\right)^2 & = \\left(\\frac{5}{4}x+\\frac{4}{3}\\right)\\left(\\frac{5}{4}x-\\frac{4}{3}\\right) \\\\\n\\frac{25}{16}x^{2}-\\frac{5}{3}x+\\frac{4}{9} & =  \\frac{25}{16}x^{2}-\\frac{16}{9} && |-\\frac{25}{16}x^{2}\\\\\n-\\frac{5}{3}x+\\frac{4}{9} & =  -\\frac{16}{9} && |-\\frac{4}{9}\\\\\n-\\frac{5}{3}x & =  -\\frac{20}{9} && | :-\\frac{5}{3}\\\\\nx & =  \\frac{4}{3}\n\\end{align*}$"], ["$\\displaystyle \\left(\\frac{2}{5}x-\\frac{4}{3}\\right)^2 = \\left(\\frac{2}{5}x+\\frac{2}{3}\\right)\\left(\\frac{2}{5}x-\\frac{2}{3}\\right)$", "$\\begin{align*}\\left(\\frac{2}{5}x-\\frac{4}{3}\\right)^2 & = \\left(\\frac{2}{5}x+\\frac{2}{3}\\right)\\left(\\frac{2}{5}x-\\frac{2}{3}\\right) \\\\\n\\frac{4}{25}x^{2}-\\frac{16}{15}x+\\frac{16}{9} & =  \\frac{4}{25}x^{2}-\\frac{4}{9} && |-\\frac{4}{25}x^{2}\\\\\n-\\frac{16}{15}x+\\frac{16}{9} & =  -\\frac{4}{9} && |-\\frac{16}{9}\\\\\n-\\frac{16}{15}x & =  -\\frac{20}{9} && | :-\\frac{16}{15}\\\\\nx & =  \\frac{25}{12}\n\\end{align*}$"], ["$\\displaystyle \\left(\\frac{3}{5}x+\\frac{5}{2}\\right)^2 = \\left(\\frac{3}{5}x-\\frac{5}{2}\\right)\\left(\\frac{3}{5}x+\\frac{5}{2}\\right)$", "$\\begin{align*}\\left(\\frac{3}{5}x+\\frac{5}{2}\\right)^2 & = \\left(\\frac{3}{5}x-\\frac{5}{2}\\right)\\left(\\frac{3}{5}x+\\frac{5}{2}\\right) \\\\\n\\frac{9}{25}x^{2}+3x+\\frac{25}{4} & =  \\frac{9}{25}x^{2}-\\frac{25}{4} && |-\\frac{9}{25}x^{2}\\\\\n3x+\\frac{25}{4} & =  -\\frac{25}{4} && |-\\frac{25}{4}\\\\\n3x & =  -\\frac{25}{2} && | :3\\\\\nx & =  -\\frac{25}{6}\n\\end{align*}$"], ["$\\displaystyle \\left(\\frac{5}{3}x-\\frac{3}{2}\\right)^2 = \\left(\\frac{5}{3}x-\\frac{3}{4}\\right)\\left(\\frac{5}{3}x+\\frac{3}{4}\\right)$", "$\\begin{align*}\\left(\\frac{5}{3}x-\\frac{3}{2}\\right)^2 & = \\left(\\frac{5}{3}x-\\frac{3}{4}\\right)\\left(\\frac{5}{3}x+\\frac{3}{4}\\right) \\\\\n\\frac{25}{9}x^{2}-5x+\\frac{9}{4} & =  \\frac{25}{9}x^{2}-\\frac{9}{16} && |-\\frac{25}{9}x^{2}\\\\\n-5x+\\frac{9}{4} & =  -\\frac{9}{16} && |-\\frac{9}{4}\\\\\n-5x & =  -\\frac{45}{16} && | :-5\\\\\nx & =  \\frac{9}{16}\n\\end{align*}$"], ["$\\displaystyle \\left(\\frac{2}{5}x-\\frac{5}{2}\\right)^2 = \\left(\\frac{2}{5}x-\\frac{3}{2}\\right)\\left(\\frac{2}{5}x+\\frac{3}{2}\\right)$", "$\\begin{align*}\\left(\\frac{2}{5}x-\\frac{5}{2}\\right)^2 & = \\left(\\frac{2}{5}x-\\frac{3}{2}\\right)\\left(\\frac{2}{5}x+\\frac{3}{2}\\right) \\\\\n\\frac{4}{25}x^{2}-2x+\\frac{25}{4} & =  \\frac{4}{25}x^{2}-\\frac{9}{4} && |-\\frac{4}{25}x^{2}\\\\\n-2x+\\frac{25}{4} & =  -\\frac{9}{4} && |-\\frac{25}{4}\\\\\n-2x & =  -\\frac{17}{2} && | :-2\\\\\nx & =  \\frac{17}{4}\n\\end{align*}$"], ["$\\displaystyle \\left(\\frac{2}{5}x+\\frac{2}{3}\\right)^2 = \\left(\\frac{2}{5}x-\\frac{4}{3}\\right)\\left(\\frac{2}{5}x+\\frac{4}{3}\\right)$", "$\\begin{align*}\\left(\\frac{2}{5}x+\\frac{2}{3}\\right)^2 & = \\left(\\frac{2}{5}x-\\frac{4}{3}\\right)\\left(\\frac{2}{5}x+\\frac{4}{3}\\right) \\\\\n\\frac{4}{25}x^{2}+\\frac{8}{15}x+\\frac{4}{9} & =  \\frac{4}{25}x^{2}-\\frac{16}{9} && |-\\frac{4}{25}x^{2}\\\\\n\\frac{8}{15}x+\\frac{4}{9} & =  -\\frac{16}{9} && |-\\frac{4}{9}\\\\\n\\frac{8}{15}x & =  -\\frac{20}{9} && | :\\frac{8}{15}\\\\\nx & =  -\\frac{25}{6}\n\\end{align*}$"]],
" <hr> ", " <hr> ");
</JS>
<HTML>
<div id="exolinGleichMitBinom"></div>

</HTML>
<hidden Lösungen>
<HTML>
<div id="sollinGleichMitBinom"></div>
<div style='font-size:12px;color:gray;'>ruby linearegleichungen.rb 3</div>
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=== Freitag 4. März 2022 ===


Ausmultiplizieren und Zusammenfassen. Achten Sie auf saubere Darstellung!<JS>miniAufgabe("#exoausmult2","#solausmult2",
[["$\\displaystyle \\left(2p-u\\right)\\left(2p^{4}-5p^{3}u+5p^{2}u^{2}+8pu^{3}+3u^{4}\\right)$", "$\\displaystyle \\begin{array}{rcrcrcrcrcrcc}4p^{5} & - & 10p^{4}u & + & 10p^{3}u^{2} & + & 16p^{2}u^{3} & + & 6pu^{4} & & & \\\\\n & - & 2p^{4}u & + & 5p^{3}u^{2} & - & 5p^{2}u^{3} & - & 8pu^{4} & - & 3u^{5} & = \\\\\n4p^{5} & - & 12p^{4}u & + & 15p^{3}u^{2} & + & 11p^{2}u^{3} & - & 2pu^{4} & - & 3u^{5} & \\\\\n\\end{array}$"], ["$\\displaystyle \\left(d-2n\\right)\\left(3d^{4}-4d^{3}n+d^{2}n^{2}-4dn^{3}-6n^{4}\\right)$", "$\\displaystyle \\begin{array}{rcrcrcrcrcrcc}3d^{5} & - & 4d^{4}n & + & d^{3}n^{2} & - & 4d^{2}n^{3} & - & 6dn^{4} & & & \\\\\n & - & 6d^{4}n & + & 8d^{3}n^{2} & - & 2d^{2}n^{3} & + & 8dn^{4} & + & 12n^{5} & = \\\\\n3d^{5} & - & 10d^{4}n & + & 9d^{3}n^{2} & - & 6d^{2}n^{3} & + & 2dn^{4} & + & 12n^{5} & \\\\\n\\end{array}$"], ["$\\displaystyle \\left(-2d+f\\right)\\left(-3d^{4}-3d^{3}f-9d^{2}f^{2}-2df^{3}-6f^{4}\\right)$", "$\\displaystyle \\begin{array}{rcrcrcrcrcrcc}6d^{5} & + & 6d^{4}f & + & 18d^{3}f^{2} & + & 4d^{2}f^{3} & + & 12df^{4} & & & \\\\\n & - & 3d^{4}f & - & 3d^{3}f^{2} & - & 9d^{2}f^{3} & - & 2df^{4} & - & 6f^{5} & = \\\\\n6d^{5} & + & 3d^{4}f & + & 15d^{3}f^{2} & - & 5d^{2}f^{3} & + & 10df^{4} & - & 6f^{5} & \\\\\n\\end{array}$"], ["$\\displaystyle \\left(-2c+e\\right)\\left(-6c^{4}+6c^{3}e+2c^{2}e^{2}+4ce^{3}-3e^{4}\\right)$", "$\\displaystyle \\begin{array}{rcrcrcrcrcrcc}12c^{5} & - & 12c^{4}e & - & 4c^{3}e^{2} & - & 8c^{2}e^{3} & + & 6ce^{4} & & & \\\\\n & - & 6c^{4}e & + & 6c^{3}e^{2} & + & 2c^{2}e^{3} & + & 4ce^{4} & - & 3e^{5} & = \\\\\n12c^{5} & - & 18c^{4}e & + & 2c^{3}e^{2} & - & 6c^{2}e^{3} & + & 10ce^{4} & - & 3e^{5} & \\\\\n\\end{array}$"], ["$\\displaystyle \\left(2a-e\\right)\\left(5a^{4}-9a^{3}e-4a^{2}e^{2}-3ae^{3}-7e^{4}\\right)$", "$\\displaystyle \\begin{array}{rcrcrcrcrcrcc}10a^{5} & - & 18a^{4}e & - & 8a^{3}e^{2} & - & 6a^{2}e^{3} & - & 14ae^{4} & & & \\\\\n & - & 5a^{4}e & + & 9a^{3}e^{2} & + & 4a^{2}e^{3} & + & 3ae^{4} & + & 7e^{5} & = \\\\\n10a^{5} & - & 23a^{4}e & + & a^{3}e^{2} & - & 2a^{2}e^{3} & - & 11ae^{4} & + & 7e^{5} & \\\\\n\\end{array}$"], ["$\\displaystyle \\left(d-2k\\right)\\left(-9d^{4}-2d^{3}k+4d^{2}k^{2}+5dk^{3}-7k^{4}\\right)$", "$\\displaystyle \\begin{array}{rcrcrcrcrcrcc}-9d^{5} & - & 2d^{4}k & + & 4d^{3}k^{2} & + & 5d^{2}k^{3} & - & 7dk^{4} & & & \\\\\n & + & 18d^{4}k & + & 4d^{3}k^{2} & - & 8d^{2}k^{3} & - & 10dk^{4} & + & 14k^{5} & = \\\\\n-9d^{5} & + & 16d^{4}k & + & 8d^{3}k^{2} & - & 3d^{2}k^{3} & - & 17dk^{4} & + & 14k^{5} & \\\\\n\\end{array}$"], ["$\\displaystyle \\left(-2e+h\\right)\\left(-4e^{4}-8e^{3}h+6e^{2}h^{2}-8eh^{3}-4h^{4}\\right)$", "$\\displaystyle \\begin{array}{rcrcrcrcrcrcc}8e^{5} & + & 16e^{4}h & - & 12e^{3}h^{2} & + & 16e^{2}h^{3} & + & 8eh^{4} & & & \\\\\n & - & 4e^{4}h & - & 8e^{3}h^{2} & + & 6e^{2}h^{3} & - & 8eh^{4} & - & 4h^{5} & = \\\\\n8e^{5} & + & 12e^{4}h & - & 20e^{3}h^{2} & + & 22e^{2}h^{3} & - & 4h^{5} & \\\\\n\\end{array}$"], ["$\\displaystyle \\left(-2c+p\\right)\\left(8c^{4}+2c^{3}p-8c^{2}p^{2}-6cp^{3}-8p^{4}\\right)$", "$\\displaystyle \\begin{array}{rcrcrcrcrcrcc}-16c^{5} & - & 4c^{4}p & + & 16c^{3}p^{2} & + & 12c^{2}p^{3} & + & 16cp^{4} & & & \\\\\n & + & 8c^{4}p & + & 2c^{3}p^{2} & - & 8c^{2}p^{3} & - & 6cp^{4} & - & 8p^{5} & = \\\\\n-16c^{5} & + & 4c^{4}p & + & 18c^{3}p^{2} & + & 4c^{2}p^{3} & + & 10cp^{4} & - & 8p^{5} & \\\\\n\\end{array}$"], ["$\\displaystyle \\left(-2c+d\\right)\\left(-3c^{4}+4c^{3}d-4c^{2}d^{2}-7cd^{3}-d^{4}\\right)$", "$\\displaystyle \\begin{array}{rcrcrcrcrcrcc}6c^{5} & - & 8c^{4}d & + & 8c^{3}d^{2} & + & 14c^{2}d^{3} & + & 2cd^{4} & & & \\\\\n & - & 3c^{4}d & + & 4c^{3}d^{2} & - & 4c^{2}d^{3} & - & 7cd^{4} & - & d^{5} & = \\\\\n6c^{5} & - & 11c^{4}d & + & 12c^{3}d^{2} & + & 10c^{2}d^{3} & - & 5cd^{4} & - & d^{5} & \\\\\n\\end{array}$"], ["$\\displaystyle \\left(2b-c\\right)\\left(5b^{4}+2b^{3}c+4b^{2}c^{2}-6bc^{3}+9c^{4}\\right)$", "$\\displaystyle \\begin{array}{rcrcrcrcrcrcc}10b^{5} & + & 4b^{4}c & + & 8b^{3}c^{2} & - & 12b^{2}c^{3} & + & 18bc^{4} & & & \\\\\n & - & 5b^{4}c & - & 2b^{3}c^{2} & - & 4b^{2}c^{3} & + & 6bc^{4} & - & 9c^{5} & = \\\\\n10b^{5} & - & b^{4}c & + & 6b^{3}c^{2} & - & 16b^{2}c^{3} & + & 24bc^{4} & - & 9c^{5} & \\\\\n\\end{array}$"]],
" <hr> ", " <hr> ");
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<div id="solausmult2"></div>
<div style='font-size:12px;color:gray;'>ruby ausmultiplizieren2.rb 2</div>
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