Ontbinden in factoren (2)

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

1. \(-b^{5}+49b^{3}\)
2. \(320y^{5}+400y^{4}+125y^{3}\)
3. \(72p^{18}-50p^{4}\)
4. \(2y^{5}-20y^{4}+50y^{3}\)
5. \(9q^{8}-49q^{2}\)
6. \(-54x^{14}+72x^{9}-24x^{4}\)
7. \(245y^{7}+560y^{6}+320y^{5}\)
8. \(320a^{13}-560a^{9}x+245a^{5}x^2\)
9. \(-245p^{14}-280p^{9}s-80p^{4}s^2\)
10. \(-5s^{5}+80s^{4}-320s^{3}\)
11. \(-25p^{10}-10p^{6}x-p^{2}x^2\)
12. \(-125p^{18}+245p^{2}\)

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

Verbetersleutel

1. \(-b^{5}+49b^{3}=-b^{3}(b^2-49)=-b^{3}(b+7)(b-7)\)
2. \(320y^{5}+400y^{4}+125y^{3}=5y^{3}(64y^{2}+80y+25)=5y^{3}(8y+5)^2\)
3. \(72p^{18}-50p^{4}=2p^{4}(36p^{14}-25)=2p^{4}(6p^7+5)(6p^7-5)\)
4. \(2y^{5}-20y^{4}+50y^{3}=2y^{3}(y^2-10y+25)=2y^{3}(y-5)^2\)
5. \(9q^{8}-49q^{2}=q^{2}(9q^{6}-49)=q^{2}(3q^3+7)(3q^3-7)\)
6. \(-54x^{14}+72x^{9}-24x^{4}=-6x^{4}(9x^{10}-12x^5+4)=-6x^{4}(3x^5-2)^2\)
7. \(245y^{7}+560y^{6}+320y^{5}=5y^{5}(49y^{2}+112y+64)=5y^{5}(7y+8)^2\)
8. \(320a^{13}-560a^{9}x+245a^{5}x^2=5a^{5}(64a^{8}-112a^4x+49x^2)=5a^{5}(8a^4-7x)^2\)
9. \(-245p^{14}-280p^{9}s-80p^{4}s^2=-5p^{4}(49p^{10}+56p^5s+16s^2)=-5p^{4}(7p^5+4s)^2\)
10. \(-5s^{5}+80s^{4}-320s^{3}=-5s^{3}(s^2-16s+64)=-5s^{3}(s-8)^2\)
11. \(-25p^{10}-10p^{6}x-p^{2}x^2=-p^{2}(25p^{8}+10p^4x+x^2)=-p^{2}(5p^4+x)^2\)
12. \(-125p^{18}+245p^{2}=-5p^{2}(25p^{16}-49)=-5p^{2}(5p^8+7)(5p^8-7)\)