Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(a^2-9\)
2. \(b^2-28b+196\)
3. \(4p^{6}-81\)
4. \(100q^{6}-260q^3+169\)
5. \(196b^{6}+364b^3+169\)
6. \(4b^{10}-81q^2\)
7. \(81b^{6}-121\)
8. \(64a^{4}-112a^2y+49y^2\)
9. \(s^2-196\)
10. \(25a^2+90a+81\)
11. \(225-196y^{4}\)
12. \(100q^{16}-1\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(a^2-9=(a-3)(a+3)\)
2. \(b^2-28b+196=(b-14)^2\)
3. \(4p^{6}-81=(2p^3+9)(2p^3-9)\)
4. \(100q^{6}-260q^3+169=(10q^3-13)^2\)
5. \(196b^{6}+364b^3+169=(14b^3+13)^2\)
6. \(4b^{10}-81q^2=(2b^5+9q)(2b^5-9q)\)
7. \(81b^{6}-121=(9b^3+11)(9b^3-11)\)
8. \(64a^{4}-112a^2y+49y^2=(8a^2-7y)^2\)
9. \(s^2-196=(s+14)(s-14)\)
10. \(25a^2+90a+81=(5a+9)^2\)
11. \(225-196y^{4}=(15-14y^2)(15+14y^2)\)
12. \(100q^{16}-1=(10q^8+1)(10q^8-1)\)