Ontbinden in factoren (2)

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

1. \(9a^{15}-a^{5}\)
2. \(-18p^{13}+24p^{8}y-8p^{3}y^2\)
3. \(-2x^{7}+36x^{6}-162x^{5}\)
4. \(-192p^{15}+240p^{10}s-75p^{5}s^2\)
5. \(-72q^{10}+98q^{2}\)
6. \(128y^{11}-224y^{8}+98y^{5}\)
7. \(-12b^{4}+3b^{2}\)
8. \(-27a^{6}-90a^{4}x-75a^{2}x^2\)
9. \(4q^{7}+20q^{5}+25q^{3}\)
10. \(45b^{4}-245b^{2}\)
11. \(50s^{10}+20s^{7}+2s^{4}\)
12. \(-45a^{15}-30a^{10}s-5a^{5}s^2\)

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

Verbetersleutel

1. \(9a^{15}-a^{5}=a^{5}(9a^{10}-1)=a^{5}(3a^5+1)(3a^5-1)\)
2. \(-18p^{13}+24p^{8}y-8p^{3}y^2=-2p^{3}(9p^{10}-12p^5y+4y^2)=-2p^{3}(3p^5-2y)^2\)
3. \(-2x^{7}+36x^{6}-162x^{5}=-2x^{5}(x^2-18x+81)=-2x^{5}(x-9)^2\)
4. \(-192p^{15}+240p^{10}s-75p^{5}s^2=-3p^{5}(64p^{10}-80p^5s+25s^2)=-3p^{5}(8p^5-5s)^2\)
5. \(-72q^{10}+98q^{2}=-2q^{2}(36q^{8}-49)=-2q^{2}(6q^4+7)(6q^4-7)\)
6. \(128y^{11}-224y^{8}+98y^{5}=2y^{5}(64y^{6}-112y^3+49)=2y^{5}(8y^3-7)^2\)
7. \(-12b^{4}+3b^{2}=-3b^{2}(4b^{2}-1)=-3b^{2}(2b+1)(2b-1)\)
8. \(-27a^{6}-90a^{4}x-75a^{2}x^2=-3a^{2}(9a^{4}+30a^2x+25x^2)=-3a^{2}(3a^2+5x)^2\)
9. \(4q^{7}+20q^{5}+25q^{3}=q^{3}(4q^{4}+20q^2+25)=q^{3}(2q^2+5)^2\)
10. \(45b^{4}-245b^{2}=5b^{2}(9b^{2}-49)=5b^{2}(3b+7)(3b-7)\)
11. \(50s^{10}+20s^{7}+2s^{4}=2s^{4}(25s^{6}+10s^3+1)=2s^{4}(5s^3+1)^2\)
12. \(-45a^{15}-30a^{10}s-5a^{5}s^2=-5a^{5}(9a^{10}+6a^5s+s^2)=-5a^{5}(3a^5+s)^2\)