Ontbinden in factoren (2)

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

1. \(96y^{9}+48y^{6}+6y^{3}\)
2. \(y^{7}+4y^{6}+4y^{5}\)
3. \(-3x^{7}+12x^{6}-12x^{5}\)
4. \(48a^{18}-3a^{4}\)
5. \(5y^{7}-245y^{5}\)
6. \(32a^{9}-112a^{7}+98a^{5}\)
7. \(-3a^{4}+54a^{3}-243a^{2}\)
8. \(-108a^{11}-36a^{8}-3a^{5}\)
9. \(-32a^{14}+2a^{4}\)
10. \(-96s^{6}+54s^{4}\)
11. \(48y^{4}-147y^{2}\)
12. \(-80p^{5}+245p^{3}\)

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

Verbetersleutel

1. \(96y^{9}+48y^{6}+6y^{3}=6y^{3}(16y^{6}+8y^3+1)=6y^{3}(4y^3+1)^2\)
2. \(y^{7}+4y^{6}+4y^{5}=y^{5}(y^2+4y+4)=y^{5}(y+2)^2\)
3. \(-3x^{7}+12x^{6}-12x^{5}=-3x^{5}(x^2-4x+4)=-3x^{5}(x-2)^2\)
4. \(48a^{18}-3a^{4}=3a^{4}(16a^{14}-1)=3a^{4}(4a^7+1)(4a^7-1)\)
5. \(5y^{7}-245y^{5}=5y^{5}(y^2-49)=5y^{5}(y+7)(y-7)\)
6. \(32a^{9}-112a^{7}+98a^{5}=2a^{5}(16a^{4}-56a^2+49)=2a^{5}(4a^2-7)^2\)
7. \(-3a^{4}+54a^{3}-243a^{2}=-3a^{2}(a^2-18a+81)=-3a^{2}(a-9)^2\)
8. \(-108a^{11}-36a^{8}-3a^{5}=-3a^{5}(36a^{6}+12a^3+1)=-3a^{5}(6a^3+1)^2\)
9. \(-32a^{14}+2a^{4}=-2a^{4}(16a^{10}-1)=-2a^{4}(4a^5+1)(4a^5-1)\)
10. \(-96s^{6}+54s^{4}=-6s^{4}(16s^{2}-9)=-6s^{4}(4s+3)(4s-3)\)
11. \(48y^{4}-147y^{2}=3y^{2}(16y^{2}-49)=3y^{2}(4y+7)(4y-7)\)
12. \(-80p^{5}+245p^{3}=-5p^{3}(16p^{2}-49)=-5p^{3}(4p+7)(4p-7)\)