Ontbinden in factoren (2)

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

1. \(48y^{4}-75y^{2}\)
2. \(-72p^{5}-120p^{4}-50p^{3}\)
3. \(45s^{8}-150s^{5}+125s^{2}\)
4. \(-125y^{5}-50y^{4}-5y^{3}\)
5. \(p^{6}-10p^{5}+25p^{4}\)
6. \(192q^{12}+144q^{8}+27q^{4}\)
7. \(-3s^{5}-24s^{4}-48s^{3}\)
8. \(96p^{10}-144p^{6}y+54p^{2}y^2\)
9. \(-24b^{5}+54b^{3}\)
10. \(-b^{4}+64b^{2}\)
11. \(36p^{4}-p^{2}\)
12. \(3a^{7}+24a^{6}+48a^{5}\)

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

Verbetersleutel

1. \(48y^{4}-75y^{2}=3y^{2}(16y^{2}-25)=3y^{2}(4y+5)(4y-5)\)
2. \(-72p^{5}-120p^{4}-50p^{3}=-2p^{3}(36p^{2}+60p+25)=-2p^{3}(6p+5)^2\)
3. \(45s^{8}-150s^{5}+125s^{2}=5s^{2}(9s^{6}-30s^3+25)=5s^{2}(3s^3-5)^2\)
4. \(-125y^{5}-50y^{4}-5y^{3}=-5y^{3}(25y^{2}+10y+1)=-5y^{3}(5y+1)^2\)
5. \(p^{6}-10p^{5}+25p^{4}=p^{4}(p^2-10p+25)=p^{4}(p-5)^2\)
6. \(192q^{12}+144q^{8}+27q^{4}=3q^{4}(64q^{8}+48q^4+9)=3q^{4}(8q^4+3)^2\)
7. \(-3s^{5}-24s^{4}-48s^{3}=-3s^{3}(s^2+8s+16)=-3s^{3}(s+4)^2\)
8. \(96p^{10}-144p^{6}y+54p^{2}y^2=6p^{2}(16p^{8}-24p^4y+9y^2)=6p^{2}(4p^4-3y)^2\)
9. \(-24b^{5}+54b^{3}=-6b^{3}(4b^{2}-9)=-6b^{3}(2b+3)(2b-3)\)
10. \(-b^{4}+64b^{2}=-b^{2}(b^2-64)=-b^{2}(b+8)(b-8)\)
11. \(36p^{4}-p^{2}=p^{2}(36p^{2}-1)=p^{2}(6p+1)(6p-1)\)
12. \(3a^{7}+24a^{6}+48a^{5}=3a^{5}(a^2+8a+16)=3a^{5}(a+4)^2\)