Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(1-100a^{10}\)
2. \(169a^{8}-156a^4+36\)
3. \(q^2-81\)
4. \(s^2-26s+169\)
5. \(100q^2-9b^{10}\)
6. \(144s^2-25\)
7. \(4b^2+52b+169\)
8. \(256p^2-480p+225\)
9. \(9q^2+78q+169\)
10. \(q^2+18q+81\)
11. \(256b^{8}+224b^4s+49s^2\)
12. \(121q^2-81a^{6}\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(1-100a^{10}=(1-10a^5)(1+10a^5)\)
2. \(169a^{8}-156a^4+36=(13a^4-6)^2\)
3. \(q^2-81=(q+9)(q-9)\)
4. \(s^2-26s+169=(s-13)^2\)
5. \(100q^2-9b^{10}=(10q-3b^5)(10q+3b^5)\)
6. \(144s^2-25=(12s+5)(12s-5)\)
7. \(4b^2+52b+169=(2b+13)^2\)
8. \(256p^2-480p+225=(16p-15)^2\)
9. \(9q^2+78q+169=(3q+13)^2\)
10. \(q^2+18q+81=(q+9)^2\)
11. \(256b^{8}+224b^4s+49s^2=(16b^4+7s)^2\)
12. \(121q^2-81a^{6}=(11q-9a^3)(11q+9a^3)\)