• UeT Nr. 7 - Binomische Formeln
  • Christian Leeser
  • 19.08.2021
  • Mittlere Reife
  • Mathematik
  • 8
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1
Wende eine binomische Formel an.
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  • a) (u+t)2\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \small (u+t)^2
  • b) (rq)2\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \small (r-q)^2
  • c) (e+f)(ef)\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \small (e+f)(e-f)
  • d) (4x9)2\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \small (4x-9)^2
  • e) (6a+7)2\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \small (6a+7)^2
  • f) (5b+11)(5b11)\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \small (5b+11)(5b-11)
Lösung
a) (u+t)2=u2+2ut+t2\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \small (u+t)^2 = u^2+2ut+t^2
b) (rq)2=r22rq+q2\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \small (r-q)^2 = r^2 - 2rq + q^2
c) (e+f)(ef)=e2f2\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \small (e+f)(e-f) = e^2 - f^2
d) (4x9)2=16x272x+81\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \small (4x-9)^2 = 16x^2-72x+81
e) (6a+7)2=36a2+84a+49\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \small (6a+7)^2 = 36a^2+84a+49
f) (5b+11)(5b11)=25b2121\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \small (5b+11)(5b-11) = 25b^2 - 121
2
Faktorisiere mithilfe einer binomschen Formel
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  • a) 16x216x+4\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \small 16x^2-16x+4
  • b) 64z2+144z+81\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \small 64z^2+144z+81
  • c) i2+8it+16t2\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \small i^2+8it+16t^2
  • d) u22ur+r2\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \small u^2-2ur+r^2
  • e) o2p2\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \small o^2-p^2
  • f) 25k236w2\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \small 25k^2-36w^2
Lösung
a) 16x216x+4=(4x2)2\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \small 16x^2-16x+4 = (4x-2)^2
b) 64z2+144z+81=(8z+9)2\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \small 64z^2+144z+81 = (8z+9)^2
c) i2+8it+16t2=(i+4t)2\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \small i^2+8it+16t^2 = (i+4t)^2
d) u22ur+r2=(ur)2\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \small u^2-2ur+r^2 = (u-r)^2
e) o2p2=(o+p)(op)\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \small o^2-p^2 = (o+p)(o-p)
f) 25k236w2=(5k+6w)(5k6w)\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \small 25k^2-36w^2 = (5k+6w)(5k-6w)
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Note