Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(1-169y^{12}\)
2. \(100s^{4}+140s^2y+49y^2\)
3. \(225p^{6}-210p^3+49\)
4. \(81a^{6}-234a^3s+169s^2\)
5. \(121-49q^{16}\)
6. \(49y^2-144a^{16}\)
7. \(169q^2-16a^{16}\)
8. \(q^2+28q+196\)
9. \(64a^{8}-112a^4p+49p^2\)
10. \(y^2+10y+25\)
11. \(100p^2-180p+81\)
12. \(100b^{8}+220b^4+121\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(1-169y^{12}=(1-13y^6)(1+13y^6)\)
2. \(100s^{4}+140s^2y+49y^2=(10s^2+7y)^2\)
3. \(225p^{6}-210p^3+49=(15p^3-7)^2\)
4. \(81a^{6}-234a^3s+169s^2=(9a^3-13s)^2\)
5. \(121-49q^{16}=(11-7q^8)(11+7q^8)\)
6. \(49y^2-144a^{16}=(7y-12a^8)(7y+12a^8)\)
7. \(169q^2-16a^{16}=(13q-4a^8)(13q+4a^8)\)
8. \(q^2+28q+196=(q+14)^2\)
9. \(64a^{8}-112a^4p+49p^2=(8a^4-7p)^2\)
10. \(y^2+10y+25=(y+5)^2\)
11. \(100p^2-180p+81=(10p-9)^2\)
12. \(100b^{8}+220b^4+121=(10b^4+11)^2\)