Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(100a^{12}-169\)
2. \(169x^{8}-390x^4+225\)
3. \(16x^{4}+8x^2+1\)
4. \(121-36s^{6}\)
5. \(64p^{8}-81s^2\)
6. \(9a^{8}-30a^4+25\)
7. \(100a^{10}+220a^5y+121y^2\)
8. \(s^2-25\)
9. \(p^2-12p+36\)
10. \(9b^{8}-16\)
11. \(16a^{6}+24a^3b+9b^2\)
12. \(196-169x^{16}\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(100a^{12}-169=(10a^6+13)(10a^6-13)\)
2. \(169x^{8}-390x^4+225=(13x^4-15)^2\)
3. \(16x^{4}+8x^2+1=(4x^2+1)^2\)
4. \(121-36s^{6}=(11-6s^3)(11+6s^3)\)
5. \(64p^{8}-81s^2=(8p^4+9s)(8p^4-9s)\)
6. \(9a^{8}-30a^4+25=(3a^4-5)^2\)
7. \(100a^{10}+220a^5y+121y^2=(10a^5+11y)^2\)
8. \(s^2-25=(s+5)(s-5)\)
9. \(p^2-12p+36=(p-6)^2\)
10. \(9b^{8}-16=(3b^4+4)(3b^4-4)\)
11. \(16a^{6}+24a^3b+9b^2=(4a^3+3b)^2\)
12. \(196-169x^{16}=(14-13x^8)(14+13x^8)\)