Aufgaben

Aufgabe 1

Wende die erste binomische Formel an.

\(324u^2+324au+81a^2\)

\(484b^2+264b+36\)

\(169+286d+121d^2\)

\(256l^2+352lr+121r^2\)

\(576n^2+240nw+25w^2\)

\(196+ 448s+256s^2\)

\(64f^2+224fz+196z^2\)

\(h^2+26hi+169i^2\)

\(289n^2+442nr+169r^2\)

\(121b^2+88bp+16p^2\)

\(9+108w+324w^2\)

\(400i^2+960hi+576h^2\)

\(400r^2+320ir+64i^2\)

\(c^2+10cd+25d^2\)

\(49+266x^2+361x^4\)

\(484s^2+396fs^2+81f^2s^2\)

\(484b^2+88bl^2+4l^4\)

\(225v^2w^2+510avw+289a^2\)

\(121e^2l^2\)

\(4t^4+92t^3+529t^2\)

\(324h^6+468h^3n+169n^2\)

\(169+416m^4+256m^8\)

\(100l^2+140l^2p+49l^2p^2\)

\(36p^2+ 84 +{49 \over p^2}\)

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Aufgabe 2

Wende die zweite binomische Formel an.

\(4h^2-60hk+225k^2\)

\(36z^2-60bz+25b^2\)

\(484i^2-836iw+361w^2\)

\(324c^2-684ch+361h^2\)

\(576a^2-720am+225m^2\)

\(169u^2+182lu+49l^2\)

\(196e^2+28ce+c^4\)

\(9s^2-18sx+9x^2\)

\(484-1100s+625s^2\)

\(100s^2-260qs^2+169q^2s^2\)

\(576w^2-384wz+64z^2\)

\(441b^2-1008bz+576z^2\)

\(256v^4+192v^2+36\)

\(49t^2-84dot+36d^2o^2\)

\(e^2-24er+144r^2\)

\(w^2-48bw+576b^2\)

\(225m^2-750m+625\)

\(36+264h+484h^2\)

\(100j^2-40jq+4q^2\)

\(361l^2-456lt+144t^2\)

\(144w^4-72h^2w^2+9h^4\)

\(64q^2+288cq+324c^2\)

\(225e^2+42+{1,96 \over e^2}\)

\(36p^2- 84 +{49 \over p^2}\)

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Aufgabe 3

Wende die dritte binomische Formel an.

\(64u^2-81a^2\)

\(4a^2-484b^2\)

\(169d^2-121\)

\(225k^2-144r^2\)

\(576v^2-49w^2\)

\(256s^2-196t^2\)

\({1 \over 64}f^2-{9 \over 49}e^2\)

\(9h^2-169i^2\)

\({25 \over 36} n^2 - 4g^2\)

\(121b^2-16p^2\)

\(9a^2-289b^2\)

\(49g^2-0,16h^2\)

\(400r^2-64i^2\)

\({1 \over 4}-b^2\)

\(49-361x^4\)

\(441t^2-81f^2t^2\)

\(144b^2-4l^4\)

\(169v^2w^2-256a^2\)

\(1715a^2d^2\)

\(4t^4-121t^2\)

\(36h^6-169n^2\)

\(25-256m^8\)

\(100l^2-49l^2p^2\)

\({100 \over 121} - {49 \over p^2}\)

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Aufgabe 4

Wende eine passende binomische Formel an.

\(3,24j^2-82,8gj+529g^2\)

\(3,24j^2-529g^2\)

\(49u^2-18,2u+1,69\)

\(4,41i^2+37,8iq+81q^2\)

\(5,76n^2-7,68fn+2,56f^2\)

\(0,25j^2-0,5jl+0,25l^2\)

\(100h^2+28hz+1,96z^2\)

\(1,44x^2+14,4hx+36h^2\)

\(4,84t^2-5,72tu+1,69u^2\)

\(0,0225-0,72u+5,76u^2\)

\(0,0529t^2-5,06gt+121g^2\)

\(100k^2-{9 \over 16}w^2\)

\({324\over 361}v^2+{252 \over 361}v+{49 \over 361}\)

\({144 \over 49}+{72\over 35}m+{9 \over 25}m^2\)

\({1 \over 9}n^2 -{14 \over 11}ln + {441\over 121}l^2\)

\({100 \over 121}+{10 \over 11}n+{1 \over 4}n^2\)

\(4m^2-{1 \over 484}b^2\)

\({1 \over 36}n^2 - {2 \over 9}gn + {4 \over 9}g^2\)

\({1 \over 4}-b^2\)

\({1 \over 49}s^2 + {5 \over 28}gs + {25 \over 64}g^2\)

\({16 \over 49}n^2-{40 \over 63}n+{25 \over 81}\)

\({4 \over 9}a^2-{9 \over 4}b^2\)

\({64 \over 81}r^2+{16\over 45}br+{1 \over 25}b^2\)

\({1 \over 144}r^2\)

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Aufgabe 5

Wende eine passende binomische Formel an, um die Summe als Produkt zu schreiben.

\((2r-3x)^2\)

\((11z+17u)\)

\((2b-9c)^2\)

\((-k+23g)^2\)

\((18j+12)^2\)

\((20c-25g)^2\)

\((14a+2)^2\)

\((1,5r+5s)^2\)

\((4s^2+1,4w)^2\)

\((0,4g+10n)^2\)

\((0,3y^2-4z)^2\)

\((2w^2+2,1f^2)^2\)

\((0,9d^2-9l)^2\)

\((20y^2-2,3k^2)^2\)

\(({1 \over 2}t-{6 \over 7}x)^2\)

\(({4 \over 9}g-{2 \over 5}a)^2\)

\(({1 \over 9}h+{2 \over 3}v)^2\)

\(({3 \over 4}y-{4 \over 9}s)^2\)

\(({1 \over 2}i-{4 \over 5}n)^2\)

\(({1 \over 4}r-{5 \over 8}i)^2\)

\(({7 \over 8}i-{5 \over 9}g)^2\)

\(({5 \over 7}r+{7 \over 9})^2\)

\(({2 \over 9}g-{5 \over 7}h)^2\)

\(({1 \over 2}j+{5 \over 6}u)^2\)

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Aufgabe 6

Ergänze die Summe um einen Summanden so, dass du sie mit Hilfe der ersten oder zweiten binomischen Formel in ein Produkt umwandeln kannst. Schreibe die geschickt ergänzte Summe anschließend als Produkt.

\(9-144b+576b^2=(3-24b)^2\)

\(400k^2+720ky+324y^2=(20k+18y)^2\)

\(p^2+44pt+484t^2=(p+22t)^2\)

\(225b^2-90bc+9c^2=(15b-3c)^2\)

\(i^2+46i+529=(i+23)^2\)

\(16w^2+64wl+64l^2=(4w+8l)^2\)

\(2,56+7,36d+5,29d^2=(1,6+2,3d)^2\)

\(100g^2-36gq+3,24q^2=(10g-1,8q)^2\)

\(4,84l^2+5,72fl+1,69f^2=(2,2l+1,3f)^2\)

\(1,69s^2-10,4sz+16z^2=(1,3s-4z)^2\)

\(4,41n^2-6,3dn+2,25d^2=(2,1n-1,5d)^2\)

\(0,81e^2-10,8be+36b^2=(0,9e-6b)^2\)

\({1 \over 100}t^2+{1 \over 14}tz+{25 \over 196}z^2=({1 \over 10}t+{5 \over 14}z)^2\)

\({16 \over 81}d^2-{2 \over 9}dq+{1 \over 16}q^2=({4 \over 9}d-{1 \over 4}q)^2\)

\({49 \over 256}v^2+{7 \over 18}vt+{16 \over 81}t^2=({7 \over 16}v+{4 \over 9}t)^2\)

\({16 \over 25}+{4 \over 5}w+{1 \over 4}w^2=({4 \over 5}+{1 \over 2}w)^2\)

\({36 \over 169}s^2+{15 \over 26}sp+{25 \over 64}p^2=({6 \over 13}s+{5 \over 8}p)^2\)

\({36 \over 121}y^2+{60 \over 77}ya+{25 \over 49}a^2=({6 \over 11}y+{5 \over 7}a)^2\)