Ontbinden in factoren (2)

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

1. \(128y^{8}+32y^{6}+2y^{4}\)
2. \(9q^{9}-12q^{6}+4q^{3}\)
3. \(-125s^{10}+320s^{4}\)
4. \(16s^{9}+8s^{7}+s^{5}\)
5. \(-75b^{4}+48b^{2}\)
6. \(-32s^{7}+18s^{5}\)
7. \(-150p^{8}-60p^{6}q-6p^{4}q^2\)
8. \(-20b^{8}+5b^{4}\)
9. \(-20q^{12}-60q^{8}s-45q^{4}s^2\)
10. \(-5s^{4}-30s^{3}-45s^{2}\)
11. \(294y^{9}-504y^{7}+216y^{5}\)
12. \(6s^{6}-294s^{4}\)

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

Verbetersleutel

1. \(128y^{8}+32y^{6}+2y^{4}=2y^{4}(64y^{4}+16y^2+1)=2y^{4}(8y^2+1)^2\)
2. \(9q^{9}-12q^{6}+4q^{3}=q^{3}(9q^{6}-12q^3+4)=q^{3}(3q^3-2)^2\)
3. \(-125s^{10}+320s^{4}=-5s^{4}(25s^{6}-64)=-5s^{4}(5s^3+8)(5s^3-8)\)
4. \(16s^{9}+8s^{7}+s^{5}=s^{5}(16s^{4}+8s^2+1)=s^{5}(4s^2+1)^2\)
5. \(-75b^{4}+48b^{2}=-3b^{2}(25b^{2}-16)=-3b^{2}(5b+4)(5b-4)\)
6. \(-32s^{7}+18s^{5}=-2s^{5}(16s^{2}-9)=-2s^{5}(4s+3)(4s-3)\)
7. \(-150p^{8}-60p^{6}q-6p^{4}q^2=-6p^{4}(25p^{4}+10p^2q+q^2)=-6p^{4}(5p^2+q)^2\)
8. \(-20b^{8}+5b^{4}=-5b^{4}(4b^{4}-1)=-5b^{4}(2b^2+1)(2b^2-1)\)
9. \(-20q^{12}-60q^{8}s-45q^{4}s^2=-5q^{4}(4q^{8}+12q^4s+9s^2)=-5q^{4}(2q^4+3s)^2\)
10. \(-5s^{4}-30s^{3}-45s^{2}=-5s^{2}(s^2+6s+9)=-5s^{2}(s+3)^2\)
11. \(294y^{9}-504y^{7}+216y^{5}=6y^{5}(49y^{4}-84y^2+36)=6y^{5}(7y^2-6)^2\)
12. \(6s^{6}-294s^{4}=6s^{4}(s^2-49)=6s^{4}(s+7)(s-7)\)