Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(225p^{10}+420p^5+196\)
2. \(81s^{10}-100\)
3. \(9q^2-100a^{12}\)
4. \(9b^2+6b+1\)
5. \(100s^{4}-49\)
6. \(64a^{4}-9\)
7. \(p^2-12p+36\)
8. \(256q^2+160q+25\)
9. \(144x^{14}-121\)
10. \(9q^{8}-30q^4s+25s^2\)
11. \(9b^{6}+24b^3+16\)
12. \(169x^2+312x+144\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(225p^{10}+420p^5+196=(15p^5+14)^2\)
2. \(81s^{10}-100=(9s^5+10)(9s^5-10)\)
3. \(9q^2-100a^{12}=(3q-10a^6)(3q+10a^6)\)
4. \(9b^2+6b+1=(3b+1)^2\)
5. \(100s^{4}-49=(10s^2+7)(10s^2-7)\)
6. \(64a^{4}-9=(8a^2+3)(8a^2-3)\)
7. \(p^2-12p+36=(p-6)^2\)
8. \(256q^2+160q+25=(16q+5)^2\)
9. \(144x^{14}-121=(12x^7+11)(12x^7-11)\)
10. \(9q^{8}-30q^4s+25s^2=(3q^4-5s)^2\)
11. \(9b^{6}+24b^3+16=(3b^3+4)^2\)
12. \(169x^2+312x+144=(13x+12)^2\)