Ontbinden in factoren (2)

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

1. \(96s^{6}-54s^{4}\)
2. \(128s^{12}-224s^{8}y+98s^{4}y^2\)
3. \(-16p^{15}+56p^{10}y-49p^{5}y^2\)
4. \(-2s^{7}+24s^{6}-72s^{5}\)
5. \(75s^{18}-108s^{4}\)
6. \(-75p^{13}+120p^{8}-48p^{3}\)
7. \(8x^{6}-98x^{2}\)
8. \(-32y^{6}+18y^{4}\)
9. \(-9q^{15}-30q^{10}-25q^{5}\)
10. \(2p^{6}+4p^{5}+2p^{4}\)
11. \(36p^{8}-60p^{6}+25p^{4}\)
12. \(s^{6}-64s^{4}\)

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

Verbetersleutel

1. \(96s^{6}-54s^{4}=6s^{4}(16s^{2}-9)=6s^{4}(4s+3)(4s-3)\)
2. \(128s^{12}-224s^{8}y+98s^{4}y^2=2s^{4}(64s^{8}-112s^4y+49y^2)=2s^{4}(8s^4-7y)^2\)
3. \(-16p^{15}+56p^{10}y-49p^{5}y^2=-p^{5}(16p^{10}-56p^5y+49y^2)=-p^{5}(4p^5-7y)^2\)
4. \(-2s^{7}+24s^{6}-72s^{5}=-2s^{5}(s^2-12s+36)=-2s^{5}(s-6)^2\)
5. \(75s^{18}-108s^{4}=3s^{4}(25s^{14}-36)=3s^{4}(5s^7+6)(5s^7-6)\)
6. \(-75p^{13}+120p^{8}-48p^{3}=-3p^{3}(25p^{10}-40p^5+16)=-3p^{3}(5p^5-4)^2\)
7. \(8x^{6}-98x^{2}=2x^{2}(4x^{4}-49)=2x^{2}(2x^2+7)(2x^2-7)\)
8. \(-32y^{6}+18y^{4}=-2y^{4}(16y^{2}-9)=-2y^{4}(4y+3)(4y-3)\)
9. \(-9q^{15}-30q^{10}-25q^{5}=-q^{5}(9q^{10}+30q^5+25)=-q^{5}(3q^5+5)^2\)
10. \(2p^{6}+4p^{5}+2p^{4}=2p^{4}(p^2+2p+1)=2p^{4}(p+1)^2\)
11. \(36p^{8}-60p^{6}+25p^{4}=p^{4}(36p^{4}-60p^2+25)=p^{4}(6p^2-5)^2\)
12. \(s^{6}-64s^{4}=s^{4}(s^2-64)=s^{4}(s-8)(s+8)\)