Ontbinden in factoren (2)

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

1. \(-150b^{6}+54b^{4}\)
2. \(216s^{9}+360s^{7}+150s^{5}\)
3. \(s^{4}-2s^{3}+s^{2}\)
4. \(49y^{10}-28y^{6}+4y^{2}\)
5. \(-96p^{9}+336p^{6}y-294p^{3}y^2\)
6. \(-b^{6}-8b^{5}-16b^{4}\)
7. \(3b^{7}+6b^{6}+3b^{5}\)
8. \(5a^{4}-180a^{2}\)
9. \(6y^{5}-24y^{4}+24y^{3}\)
10. \(54s^{19}-294s^{5}\)
11. \(3p^{7}-12p^{5}\)
12. \(-2p^{4}+4p^{3}-2p^{2}\)

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

Verbetersleutel

1. \(-150b^{6}+54b^{4}=-6b^{4}(25b^{2}-9)=-6b^{4}(5b+3)(5b-3)\)
2. \(216s^{9}+360s^{7}+150s^{5}=6s^{5}(36s^{4}+60s^2+25)=6s^{5}(6s^2+5)^2\)
3. \(s^{4}-2s^{3}+s^{2}=s^{2}(s^2-2s+1)=s^{2}(s-1)^2\)
4. \(49y^{10}-28y^{6}+4y^{2}=y^{2}(49y^{8}-28y^4+4)=y^{2}(7y^4-2)^2\)
5. \(-96p^{9}+336p^{6}y-294p^{3}y^2=-6p^{3}(16p^{6}-56p^3y+49y^2)=-6p^{3}(4p^3-7y)^2\)
6. \(-b^{6}-8b^{5}-16b^{4}=-b^{4}(b^2+8b+16)=-b^{4}(b+4)^2\)
7. \(3b^{7}+6b^{6}+3b^{5}=3b^{5}(b^2+2b+1)=3b^{5}(b+1)^2\)
8. \(5a^{4}-180a^{2}=5a^{2}(a^2-36)=5a^{2}(a-6)(a+6)\)
9. \(6y^{5}-24y^{4}+24y^{3}=6y^{3}(y^2-4y+4)=6y^{3}(y-2)^2\)
10. \(54s^{19}-294s^{5}=6s^{5}(9s^{14}-49)=6s^{5}(3s^7+7)(3s^7-7)\)
11. \(3p^{7}-12p^{5}=3p^{5}(p^2-4)=3p^{5}(p+2)(p-2)\)
12. \(-2p^{4}+4p^{3}-2p^{2}=-2p^{2}(p^2-2p+1)=-2p^{2}(p-1)^2\)