Ontbinden in factoren (2)

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

1. \(3q^{4}-12q^{2}\)
2. \(-12p^{4}+3p^{2}\)
3. \(-64a^{4}-16a^{3}-a^{2}\)
4. \(-4p^{4}+25p^{2}\)
5. \(96b^{7}+48b^{6}+6b^{5}\)
6. \(96b^{4}-144b^{3}+54b^{2}\)
7. \(54a^{15}-180a^{10}y+150a^{5}y^2\)
8. \(-16a^{8}+24a^{5}-9a^{2}\)
9. \(3s^{6}-6s^{5}+3s^{4}\)
10. \(-54p^{6}+180p^{4}s-150p^{2}s^2\)
11. \(25a^{6}-36a^{4}\)
12. \(9s^{16}-4s^{2}\)

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

Verbetersleutel

1. \(3q^{4}-12q^{2}=3q^{2}(q^2-4)=3q^{2}(q+2)(q-2)\)
2. \(-12p^{4}+3p^{2}=-3p^{2}(4p^{2}-1)=-3p^{2}(2p+1)(2p-1)\)
3. \(-64a^{4}-16a^{3}-a^{2}=-a^{2}(64a^{2}+16a+1)=-a^{2}(8a+1)^2\)
4. \(-4p^{4}+25p^{2}=-p^{2}(4p^{2}-25)=-p^{2}(2p+5)(2p-5)\)
5. \(96b^{7}+48b^{6}+6b^{5}=6b^{5}(16b^{2}+8b+1)=6b^{5}(4b+1)^2\)
6. \(96b^{4}-144b^{3}+54b^{2}=6b^{2}(16b^{2}-24b+9)=6b^{2}(4b-3)^2\)
7. \(54a^{15}-180a^{10}y+150a^{5}y^2=6a^{5}(9a^{10}-30a^5y+25y^2)=6a^{5}(3a^5-5y)^2\)
8. \(-16a^{8}+24a^{5}-9a^{2}=-a^{2}(16a^{6}-24a^3+9)=-a^{2}(4a^3-3)^2\)
9. \(3s^{6}-6s^{5}+3s^{4}=3s^{4}(s^2-2s+1)=3s^{4}(s-1)^2\)
10. \(-54p^{6}+180p^{4}s-150p^{2}s^2=-6p^{2}(9p^{4}-30p^2s+25s^2)=-6p^{2}(3p^2-5s)^2\)
11. \(25a^{6}-36a^{4}=a^{4}(25a^{2}-36)=a^{4}(5a+6)(5a-6)\)
12. \(9s^{16}-4s^{2}=s^{2}(9s^{14}-4)=s^{2}(3s^7+2)(3s^7-2)\)