Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(256a^{8}-96a^4s+9s^2\)
2. \(121b^2+308b+196\)
3. \(p^2-4\)
4. \(b^2-25\)
5. \(225q^2-64p^{14}\)
6. \(225s^2-49a^{6}\)
7. \(p^2-1\)
8. \(s^2-25\)
9. \(16p^{8}-24p^4s+9s^2\)
10. \(16a^{10}+24a^5q+9q^2\)
11. \(144-121x^{4}\)
12. \(9a^{4}-12a^2+4\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(256a^{8}-96a^4s+9s^2=(16a^4-3s)^2\)
2. \(121b^2+308b+196=(11b+14)^2\)
3. \(p^2-4=(p-2)(p+2)\)
4. \(b^2-25=(b+5)(b-5)\)
5. \(225q^2-64p^{14}=(15q-8p^7)(15q+8p^7)\)
6. \(225s^2-49a^{6}=(15s-7a^3)(15s+7a^3)\)
7. \(p^2-1=(p+1)(p-1)\)
8. \(s^2-25=(s-5)(s+5)\)
9. \(16p^{8}-24p^4s+9s^2=(4p^4-3s)^2\)
10. \(16a^{10}+24a^5q+9q^2=(4a^5+3q)^2\)
11. \(144-121x^{4}=(12-11x^2)(12+11x^2)\)
12. \(9a^{4}-12a^2+4=(3a^2-2)^2\)