Ontbinden in factoren (2)

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

1. \(-16a^{14}+a^{2}\)
2. \(-8p^{9}-8p^{6}y-2p^{3}y^2\)
3. \(128p^{6}-224p^{5}+98p^{4}\)
4. \(-180x^{8}-60x^{6}-5x^{4}\)
5. \(9b^{6}+42b^{5}+49b^{4}\)
6. \(-5b^{6}+125b^{4}\)
7. \(-75b^{15}+108b^{5}\)
8. \(2p^{6}+12p^{5}+18p^{4}\)
9. \(2y^{4}-32y^{2}\)
10. \(-150s^{6}+6s^{4}\)
11. \(108x^{4}-3x^{2}\)
12. \(12q^{13}+12q^{9}y+3q^{5}y^2\)

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

Verbetersleutel

1. \(-16a^{14}+a^{2}=-a^{2}(16a^{12}-1)=-a^{2}(4a^6+1)(4a^6-1)\)
2. \(-8p^{9}-8p^{6}y-2p^{3}y^2=-2p^{3}(4p^{6}+4p^3y+y^2)=-2p^{3}(2p^3+y)^2\)
3. \(128p^{6}-224p^{5}+98p^{4}=2p^{4}(64p^{2}-112p+49)=2p^{4}(8p-7)^2\)
4. \(-180x^{8}-60x^{6}-5x^{4}=-5x^{4}(36x^{4}+12x^2+1)=-5x^{4}(6x^2+1)^2\)
5. \(9b^{6}+42b^{5}+49b^{4}=b^{4}(9b^{2}+42b+49)=b^{4}(3b+7)^2\)
6. \(-5b^{6}+125b^{4}=-5b^{4}(b^2-25)=-5b^{4}(b-5)(b+5)\)
7. \(-75b^{15}+108b^{5}=-3b^{5}(25b^{10}-36)=-3b^{5}(5b^5+6)(5b^5-6)\)
8. \(2p^{6}+12p^{5}+18p^{4}=2p^{4}(p^2+6p+9)=2p^{4}(p+3)^2\)
9. \(2y^{4}-32y^{2}=2y^{2}(y^2-16)=2y^{2}(y+4)(y-4)\)
10. \(-150s^{6}+6s^{4}=-6s^{4}(25s^{2}-1)=-6s^{4}(5s+1)(5s-1)\)
11. \(108x^{4}-3x^{2}=3x^{2}(36x^{2}-1)=3x^{2}(6x+1)(6x-1)\)
12. \(12q^{13}+12q^{9}y+3q^{5}y^2=3q^{5}(4q^{8}+4q^4y+y^2)=3q^{5}(2q^4+y)^2\)