Ontbinden in factoren (2)

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

1. \(-25b^{6}+16b^{4}\)
2. \(128s^{14}+160s^{9}+50s^{4}\)
3. \(-16b^{5}+25b^{3}\)
4. \(-108x^{14}+75x^{2}\)
5. \(-54p^{6}+294p^{4}\)
6. \(-45s^{5}+5s^{3}\)
7. \(4p^{9}-25p^{5}\)
8. \(-80b^{21}+45b^{5}\)
9. \(-150b^{6}+294b^{4}\)
10. \(5p^{4}-20p^{2}\)
11. \(36x^{10}-60x^{6}y+25x^{2}y^2\)
12. \(216s^{15}-6s^{3}\)

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

Verbetersleutel

1. \(-25b^{6}+16b^{4}=-b^{4}(25b^{2}-16)=-b^{4}(5b+4)(5b-4)\)
2. \(128s^{14}+160s^{9}+50s^{4}=2s^{4}(64s^{10}+80s^5+25)=2s^{4}(8s^5+5)^2\)
3. \(-16b^{5}+25b^{3}=-b^{3}(16b^{2}-25)=-b^{3}(4b+5)(4b-5)\)
4. \(-108x^{14}+75x^{2}=-3x^{2}(36x^{12}-25)=-3x^{2}(6x^6+5)(6x^6-5)\)
5. \(-54p^{6}+294p^{4}=-6p^{4}(9p^{2}-49)=-6p^{4}(3p+7)(3p-7)\)
6. \(-45s^{5}+5s^{3}=-5s^{3}(9s^{2}-1)=-5s^{3}(3s+1)(3s-1)\)
7. \(4p^{9}-25p^{5}=p^{5}(4p^{4}-25)=p^{5}(2p^2+5)(2p^2-5)\)
8. \(-80b^{21}+45b^{5}=-5b^{5}(16b^{16}-9)=-5b^{5}(4b^8+3)(4b^8-3)\)
9. \(-150b^{6}+294b^{4}=-6b^{4}(25b^{2}-49)=-6b^{4}(5b+7)(5b-7)\)
10. \(5p^{4}-20p^{2}=5p^{2}(p^2-4)=5p^{2}(p+2)(p-2)\)
11. \(36x^{10}-60x^{6}y+25x^{2}y^2=x^{2}(36x^{8}-60x^4y+25y^2)=x^{2}(6x^4-5y)^2\)
12. \(216s^{15}-6s^{3}=6s^{3}(36s^{12}-1)=6s^{3}(6s^6+1)(6s^6-1)\)