Ontbinden in factoren (2)

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Zonder de gemeenschappelijke factor af. Ontbind verder in factoren indien mogelijk.

1. \(18y^{14}-2y^{2}\)
2. \(96s^{7}-336s^{6}+294s^{5}\)
3. \(-45q^{6}-30q^{4}-5q^{2}\)
4. \(6q^{6}-6q^{4}\)
5. \(245a^{12}-420a^{8}+180a^{4}\)
6. \(75p^{17}-3p^{3}\)
7. \(-y^{7}-16y^{6}-64y^{5}\)
8. \(32s^{21}-2s^{5}\)
9. \(180s^{6}+60s^{5}+5s^{4}\)
10. \(-18p^{13}+60p^{8}-50p^{3}\)
11. \(-384q^{12}-96q^{8}s-6q^{4}s^2\)
12. \(-q^{7}+4q^{6}-4q^{5}\)

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Zonder de gemeenschappelijke factor af. Ontbind verder in factoren indien mogelijk.

Verbetersleutel

1. \(18y^{14}-2y^{2}=2y^{2}(9y^{12}-1)=2y^{2}(3y^6+1)(3y^6-1)\)
2. \(96s^{7}-336s^{6}+294s^{5}=6s^{5}(16s^{2}-56s+49)=6s^{5}(4s-7)^2\)
3. \(-45q^{6}-30q^{4}-5q^{2}=-5q^{2}(9q^{4}+6q^2+1)=-5q^{2}(3q^2+1)^2\)
4. \(6q^{6}-6q^{4}=6q^{4}(q^2-1)=6q^{4}(q+1)(q-1)\)
5. \(245a^{12}-420a^{8}+180a^{4}=5a^{4}(49a^{8}-84a^4+36)=5a^{4}(7a^4-6)^2\)
6. \(75p^{17}-3p^{3}=3p^{3}(25p^{14}-1)=3p^{3}(5p^7+1)(5p^7-1)\)
7. \(-y^{7}-16y^{6}-64y^{5}=-y^{5}(y^2+16y+64)=-y^{5}(y+8)^2\)
8. \(32s^{21}-2s^{5}=2s^{5}(16s^{16}-1)=2s^{5}(4s^8+1)(4s^8-1)\)
9. \(180s^{6}+60s^{5}+5s^{4}=5s^{4}(36s^{2}+12s+1)=5s^{4}(6s+1)^2\)
10. \(-18p^{13}+60p^{8}-50p^{3}=-2p^{3}(9p^{10}-30p^5+25)=-2p^{3}(3p^5-5)^2\)
11. \(-384q^{12}-96q^{8}s-6q^{4}s^2=-6q^{4}(64q^{8}+16q^4s+s^2)=-6q^{4}(8q^4+s)^2\)
12. \(-q^{7}+4q^{6}-4q^{5}=-q^{5}(q^2-4q+4)=-q^{5}(q-2)^2\)