Ontbinden in factoren (2)

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

1. \(-54a^{7}+180a^{6}-150a^{5}\)
2. \(27q^{15}-75q^{3}\)
3. \(24y^{7}-150y^{5}\)
4. \(294q^{11}+420q^{7}+150q^{3}\)
5. \(75b^{19}-147b^{5}\)
6. \(-5s^{7}+20s^{5}\)
7. \(-16y^{15}+49y^{3}\)
8. \(4b^{6}-9b^{4}\)
9. \(-5q^{4}+5q^{2}\)
10. \(-6s^{6}-60s^{5}-150s^{4}\)
11. \(-72p^{17}+50p^{5}\)
12. \(36q^{18}-25q^{4}\)

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

Verbetersleutel

1. \(-54a^{7}+180a^{6}-150a^{5}=-6a^{5}(9a^{2}-30a+25)=-6a^{5}(3a-5)^2\)
2. \(27q^{15}-75q^{3}=3q^{3}(9q^{12}-25)=3q^{3}(3q^6+5)(3q^6-5)\)
3. \(24y^{7}-150y^{5}=6y^{5}(4y^{2}-25)=6y^{5}(2y+5)(2y-5)\)
4. \(294q^{11}+420q^{7}+150q^{3}=6q^{3}(49q^{8}+70q^4+25)=6q^{3}(7q^4+5)^2\)
5. \(75b^{19}-147b^{5}=3b^{5}(25b^{14}-49)=3b^{5}(5b^7+7)(5b^7-7)\)
6. \(-5s^{7}+20s^{5}=-5s^{5}(s^2-4)=-5s^{5}(s+2)(s-2)\)
7. \(-16y^{15}+49y^{3}=-y^{3}(16y^{12}-49)=-y^{3}(4y^6+7)(4y^6-7)\)
8. \(4b^{6}-9b^{4}=b^{4}(4b^{2}-9)=b^{4}(2b+3)(2b-3)\)
9. \(-5q^{4}+5q^{2}=-5q^{2}(q^2-1)=-5q^{2}(q+1)(q-1)\)
10. \(-6s^{6}-60s^{5}-150s^{4}=-6s^{4}(s^2+10s+25)=-6s^{4}(s+5)^2\)
11. \(-72p^{17}+50p^{5}=-2p^{5}(36p^{12}-25)=-2p^{5}(6p^6+5)(6p^6-5)\)
12. \(36q^{18}-25q^{4}=q^{4}(36q^{14}-25)=q^{4}(6q^7+5)(6q^7-5)\)