Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(121p^{4}+22p^2q+1q^2\)
2. \(p^2-49\)
3. \(64s^{8}+240s^4+225\)
4. \(81x^2-256s^{12}\)
5. \(196a^2-25\)
6. \(b^2-9\)
7. \(25p^{4}-140p^2+196\)
8. \(100p^{4}+260p^2+169\)
9. \(p^2-25\)
10. \(9-16a^{10}\)
11. \(100s^2-180s+81\)
12. \(196b^{10}+252b^5p+81p^2\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(121p^{4}+22p^2q+1q^2=(11p^2+q)^2\)
2. \(p^2-49=(p-7)(p+7)\)
3. \(64s^{8}+240s^4+225=(8s^4+15)^2\)
4. \(81x^2-256s^{12}=(9x-16s^6)(9x+16s^6)\)
5. \(196a^2-25=(14a+5)(14a-5)\)
6. \(b^2-9=(b-3)(b+3)\)
7. \(25p^{4}-140p^2+196=(5p^2-14)^2\)
8. \(100p^{4}+260p^2+169=(10p^2+13)^2\)
9. \(p^2-25=(p-5)(p+5)\)
10. \(9-16a^{10}=(3-4a^5)(3+4a^5)\)
11. \(100s^2-180s+81=(10s-9)^2\)
12. \(196b^{10}+252b^5p+81p^2=(14b^5+9p)^2\)