Ontbinden in factoren (2)

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

1. \(3p^{7}-27p^{5}\)
2. \(48p^{9}-27p^{5}\)
3. \(3x^{7}-54x^{6}+243x^{5}\)
4. \(-180a^{6}-60a^{4}p-5a^{2}p^2\)
5. \(108b^{6}-75b^{4}\)
6. \(5p^{5}-320p^{3}\)
7. \(5p^{6}-80p^{5}+320p^{4}\)
8. \(-b^{6}+8b^{5}-16b^{4}\)
9. \(32x^{6}-98x^{4}\)
10. \(-54s^{6}+150s^{4}\)
11. \(-180s^{16}+125s^{4}\)
12. \(-125b^{13}+200b^{8}y-80b^{3}y^2\)

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

Verbetersleutel

1. \(3p^{7}-27p^{5}=3p^{5}(p^2-9)=3p^{5}(p-3)(p+3)\)
2. \(48p^{9}-27p^{5}=3p^{5}(16p^{4}-9)=3p^{5}(4p^2+3)(4p^2-3)\)
3. \(3x^{7}-54x^{6}+243x^{5}=3x^{5}(x^2-18x+81)=3x^{5}(x-9)^2\)
4. \(-180a^{6}-60a^{4}p-5a^{2}p^2=-5a^{2}(36a^{4}+12a^2p+p^2)=-5a^{2}(6a^2+p)^2\)
5. \(108b^{6}-75b^{4}=3b^{4}(36b^{2}-25)=3b^{4}(6b+5)(6b-5)\)
6. \(5p^{5}-320p^{3}=5p^{3}(p^2-64)=5p^{3}(p-8)(p+8)\)
7. \(5p^{6}-80p^{5}+320p^{4}=5p^{4}(p^2-16p+64)=5p^{4}(p-8)^2\)
8. \(-b^{6}+8b^{5}-16b^{4}=-b^{4}(b^2-8b+16)=-b^{4}(b-4)^2\)
9. \(32x^{6}-98x^{4}=2x^{4}(16x^{2}-49)=2x^{4}(4x+7)(4x-7)\)
10. \(-54s^{6}+150s^{4}=-6s^{4}(9s^{2}-25)=-6s^{4}(3s+5)(3s-5)\)
11. \(-180s^{16}+125s^{4}=-5s^{4}(36s^{12}-25)=-5s^{4}(6s^6+5)(6s^6-5)\)
12. \(-125b^{13}+200b^{8}y-80b^{3}y^2=-5b^{3}(25b^{10}-40b^5y+16y^2)=-5b^{3}(5b^5-4y)^2\)