Ontbinden in factoren (2)

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

1. \(p^{4}-16p^{2}\)
2. \(-180q^{7}+125q^{5}\)
3. \(-36b^{10}+60b^{6}-25b^{2}\)
4. \(-6q^{5}+384q^{3}\)
5. \(2s^{5}-8s^{3}\)
6. \(-54p^{15}+150p^{3}\)
7. \(-8p^{19}+50p^{5}\)
8. \(12p^{13}+60p^{8}+75p^{3}\)
9. \(-5p^{7}-30p^{6}-45p^{5}\)
10. \(-27q^{6}+36q^{4}-12q^{2}\)
11. \(-150q^{7}-360q^{5}s-216q^{3}s^2\)
12. \(-75q^{7}-90q^{5}-27q^{3}\)

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

Verbetersleutel

1. \(p^{4}-16p^{2}=p^{2}(p^2-16)=p^{2}(p+4)(p-4)\)
2. \(-180q^{7}+125q^{5}=-5q^{5}(36q^{2}-25)=-5q^{5}(6q+5)(6q-5)\)
3. \(-36b^{10}+60b^{6}-25b^{2}=-b^{2}(36b^{8}-60b^4+25)=-b^{2}(6b^4-5)^2\)
4. \(-6q^{5}+384q^{3}=-6q^{3}(q^2-64)=-6q^{3}(q-8)(q+8)\)
5. \(2s^{5}-8s^{3}=2s^{3}(s^2-4)=2s^{3}(s+2)(s-2)\)
6. \(-54p^{15}+150p^{3}=-6p^{3}(9p^{12}-25)=-6p^{3}(3p^6+5)(3p^6-5)\)
7. \(-8p^{19}+50p^{5}=-2p^{5}(4p^{14}-25)=-2p^{5}(2p^7+5)(2p^7-5)\)
8. \(12p^{13}+60p^{8}+75p^{3}=3p^{3}(4p^{10}+20p^5+25)=3p^{3}(2p^5+5)^2\)
9. \(-5p^{7}-30p^{6}-45p^{5}=-5p^{5}(p^2+6p+9)=-5p^{5}(p+3)^2\)
10. \(-27q^{6}+36q^{4}-12q^{2}=-3q^{2}(9q^{4}-12q^2+4)=-3q^{2}(3q^2-2)^2\)
11. \(-150q^{7}-360q^{5}s-216q^{3}s^2=-6q^{3}(25q^{4}+60q^2s+36s^2)=-6q^{3}(5q^2+6s)^2\)
12. \(-75q^{7}-90q^{5}-27q^{3}=-3q^{3}(25q^{4}+30q^2+9)=-3q^{3}(5q^2+3)^2\)