Ontbinden in factoren (2)

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

1. \(-72q^{6}+98q^{4}\)
2. \(-216q^{18}+294q^{4}\)
3. \(5a^{6}+20a^{5}+20a^{4}\)
4. \(5s^{4}+80s^{3}+320s^{2}\)
5. \(6s^{7}-294s^{5}\)
6. \(8s^{20}-50s^{4}\)
7. \(27q^{7}-90q^{5}+75q^{3}\)
8. \(5q^{6}-245q^{4}\)
9. \(-45s^{6}-210s^{5}-245s^{4}\)
10. \(216y^{19}-150y^{3}\)
11. \(b^{7}-4b^{6}+4b^{5}\)
12. \(80a^{9}-280a^{6}+245a^{3}\)

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

Verbetersleutel

1. \(-72q^{6}+98q^{4}=-2q^{4}(36q^{2}-49)=-2q^{4}(6q+7)(6q-7)\)
2. \(-216q^{18}+294q^{4}=-6q^{4}(36q^{14}-49)=-6q^{4}(6q^7+7)(6q^7-7)\)
3. \(5a^{6}+20a^{5}+20a^{4}=5a^{4}(a^2+4a+4)=5a^{4}(a+2)^2\)
4. \(5s^{4}+80s^{3}+320s^{2}=5s^{2}(s^2+16s+64)=5s^{2}(s+8)^2\)
5. \(6s^{7}-294s^{5}=6s^{5}(s^2-49)=6s^{5}(s-7)(s+7)\)
6. \(8s^{20}-50s^{4}=2s^{4}(4s^{16}-25)=2s^{4}(2s^8+5)(2s^8-5)\)
7. \(27q^{7}-90q^{5}+75q^{3}=3q^{3}(9q^{4}-30q^2+25)=3q^{3}(3q^2-5)^2\)
8. \(5q^{6}-245q^{4}=5q^{4}(q^2-49)=5q^{4}(q-7)(q+7)\)
9. \(-45s^{6}-210s^{5}-245s^{4}=-5s^{4}(9s^{2}+42s+49)=-5s^{4}(3s+7)^2\)
10. \(216y^{19}-150y^{3}=6y^{3}(36y^{16}-25)=6y^{3}(6y^8+5)(6y^8-5)\)
11. \(b^{7}-4b^{6}+4b^{5}=b^{5}(b^2-4b+4)=b^{5}(b-2)^2\)
12. \(80a^{9}-280a^{6}+245a^{3}=5a^{3}(16a^{6}-56a^3+49)=5a^{3}(4a^3-7)^2\)