Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(p^2-4\)
2. \(196b^{12}-81q^2\)
3. \(q^2-28q+196\)
4. \(16q^{10}+8q^5+1\)
5. \(144a^{4}+264a^2s+121s^2\)
6. \(144a^{8}-264a^4+121\)
7. \(16s^{10}+56s^5+49\)
8. \(64p^2+144p+81\)
9. \(49p^{12}-4s^2\)
10. \(121-36x^{4}\)
11. \(256p^{14}-121\)
12. \(25a^{8}-140a^4q+196q^2\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(p^2-4=(p+2)(p-2)\)
2. \(196b^{12}-81q^2=(14b^6+9q)(14b^6-9q)\)
3. \(q^2-28q+196=(q-14)^2\)
4. \(16q^{10}+8q^5+1=(4q^5+1)^2\)
5. \(144a^{4}+264a^2s+121s^2=(12a^2+11s)^2\)
6. \(144a^{8}-264a^4+121=(12a^4-11)^2\)
7. \(16s^{10}+56s^5+49=(4s^5+7)^2\)
8. \(64p^2+144p+81=(8p+9)^2\)
9. \(49p^{12}-4s^2=(7p^6+2s)(7p^6-2s)\)
10. \(121-36x^{4}=(11-6x^2)(11+6x^2)\)
11. \(256p^{14}-121=(16p^7+11)(16p^7-11)\)
12. \(25a^{8}-140a^4q+196q^2=(5a^4-14q)^2\)