Ontbinden in factoren (2)

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

1. \(125s^{8}-5s^{4}\)
2. \(-54y^{6}+180y^{5}-150y^{4}\)
3. \(54s^{9}+36s^{6}y+6s^{3}y^2\)
4. \(-16b^{6}+b^{4}\)
5. \(80a^{11}-120a^{7}s+45a^{3}s^2\)
6. \(-3y^{7}+18y^{6}-27y^{5}\)
7. \(-20s^{6}-20s^{5}-5s^{4}\)
8. \(-50y^{5}+72y^{3}\)
9. \(-9a^{7}-12a^{5}q-4a^{3}q^2\)
10. \(54b^{6}-180b^{4}+150b^{2}\)
11. \(54b^{9}+144b^{7}+96b^{5}\)
12. \(-128s^{10}-32s^{7}y-2s^{4}y^2\)

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

Verbetersleutel

1. \(125s^{8}-5s^{4}=5s^{4}(25s^{4}-1)=5s^{4}(5s^2+1)(5s^2-1)\)
2. \(-54y^{6}+180y^{5}-150y^{4}=-6y^{4}(9y^{2}-30y+25)=-6y^{4}(3y-5)^2\)
3. \(54s^{9}+36s^{6}y+6s^{3}y^2=6s^{3}(9s^{6}+6s^3y+y^2)=6s^{3}(3s^3+y)^2\)
4. \(-16b^{6}+b^{4}=-b^{4}(16b^{2}-1)=-b^{4}(4b+1)(4b-1)\)
5. \(80a^{11}-120a^{7}s+45a^{3}s^2=5a^{3}(16a^{8}-24a^4s+9s^2)=5a^{3}(4a^4-3s)^2\)
6. \(-3y^{7}+18y^{6}-27y^{5}=-3y^{5}(y^2-6y+9)=-3y^{5}(y-3)^2\)
7. \(-20s^{6}-20s^{5}-5s^{4}=-5s^{4}(4s^{2}+4s+1)=-5s^{4}(2s+1)^2\)
8. \(-50y^{5}+72y^{3}=-2y^{3}(25y^{2}-36)=-2y^{3}(5y+6)(5y-6)\)
9. \(-9a^{7}-12a^{5}q-4a^{3}q^2=-a^{3}(9a^{4}+12a^2q+4q^2)=-a^{3}(3a^2+2q)^2\)
10. \(54b^{6}-180b^{4}+150b^{2}=6b^{2}(9b^{4}-30b^2+25)=6b^{2}(3b^2-5)^2\)
11. \(54b^{9}+144b^{7}+96b^{5}=6b^{5}(9b^{4}+24b^2+16)=6b^{5}(3b^2+4)^2\)
12. \(-128s^{10}-32s^{7}y-2s^{4}y^2=-2s^{4}(64s^{6}+16s^3y+y^2)=-2s^{4}(8s^3+y)^2\)