Ontbinden in factoren (2)

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

1. \(-4y^{13}+49y^{3}\)
2. \(-2p^{4}+98p^{2}\)
3. \(-54q^{9}+72q^{6}-24q^{3}\)
4. \(5p^{4}+50p^{3}+125p^{2}\)
5. \(108y^{12}-180y^{7}+75y^{2}\)
6. \(125y^{7}-350y^{6}+245y^{5}\)
7. \(18b^{6}-2b^{4}\)
8. \(-6b^{7}+384b^{5}\)
9. \(-45x^{13}+245x^{3}\)
10. \(18s^{10}-60s^{6}y+50s^{2}y^2\)
11. \(-3a^{5}-24a^{4}-48a^{3}\)
12. \(24y^{4}-150y^{2}\)

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

Verbetersleutel

1. \(-4y^{13}+49y^{3}=-y^{3}(4y^{10}-49)=-y^{3}(2y^5+7)(2y^5-7)\)
2. \(-2p^{4}+98p^{2}=-2p^{2}(p^2-49)=-2p^{2}(p-7)(p+7)\)
3. \(-54q^{9}+72q^{6}-24q^{3}=-6q^{3}(9q^{6}-12q^3+4)=-6q^{3}(3q^3-2)^2\)
4. \(5p^{4}+50p^{3}+125p^{2}=5p^{2}(p^2+10p+25)=5p^{2}(p+5)^2\)
5. \(108y^{12}-180y^{7}+75y^{2}=3y^{2}(36y^{10}-60y^5+25)=3y^{2}(6y^5-5)^2\)
6. \(125y^{7}-350y^{6}+245y^{5}=5y^{5}(25y^{2}-70y+49)=5y^{5}(5y-7)^2\)
7. \(18b^{6}-2b^{4}=2b^{4}(9b^{2}-1)=2b^{4}(3b+1)(3b-1)\)
8. \(-6b^{7}+384b^{5}=-6b^{5}(b^2-64)=-6b^{5}(b+8)(b-8)\)
9. \(-45x^{13}+245x^{3}=-5x^{3}(9x^{10}-49)=-5x^{3}(3x^5+7)(3x^5-7)\)
10. \(18s^{10}-60s^{6}y+50s^{2}y^2=2s^{2}(9s^{8}-30s^4y+25y^2)=2s^{2}(3s^4-5y)^2\)
11. \(-3a^{5}-24a^{4}-48a^{3}=-3a^{3}(a^2+8a+16)=-3a^{3}(a+4)^2\)
12. \(24y^{4}-150y^{2}=6y^{2}(4y^{2}-25)=6y^{2}(2y+5)(2y-5)\)