Ontbinden in factoren (2)

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

1. \(18s^{7}+48s^{6}+32s^{5}\)
2. \(-3q^{4}+48q^{2}\)
3. \(12p^{5}-3p^{3}\)
4. \(-2p^{4}-24p^{3}-72p^{2}\)
5. \(48q^{8}-27q^{2}\)
6. \(96p^{13}-150p^{3}\)
7. \(150p^{11}+180p^{8}y+54p^{5}y^2\)
8. \(9a^{12}-16a^{4}\)
9. \(108x^{8}-75x^{4}\)
10. \(2p^{6}+12p^{5}+18p^{4}\)
11. \(3a^{5}-192a^{3}\)
12. \(-98y^{4}+252y^{3}-162y^{2}\)

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

Verbetersleutel

1. \(18s^{7}+48s^{6}+32s^{5}=2s^{5}(9s^{2}+24s+16)=2s^{5}(3s+4)^2\)
2. \(-3q^{4}+48q^{2}=-3q^{2}(q^2-16)=-3q^{2}(q-4)(q+4)\)
3. \(12p^{5}-3p^{3}=3p^{3}(4p^{2}-1)=3p^{3}(2p+1)(2p-1)\)
4. \(-2p^{4}-24p^{3}-72p^{2}=-2p^{2}(p^2+12p+36)=-2p^{2}(p+6)^2\)
5. \(48q^{8}-27q^{2}=3q^{2}(16q^{6}-9)=3q^{2}(4q^3+3)(4q^3-3)\)
6. \(96p^{13}-150p^{3}=6p^{3}(16p^{10}-25)=6p^{3}(4p^5+5)(4p^5-5)\)
7. \(150p^{11}+180p^{8}y+54p^{5}y^2=6p^{5}(25p^{6}+30p^3y+9y^2)=6p^{5}(5p^3+3y)^2\)
8. \(9a^{12}-16a^{4}=a^{4}(9a^{8}-16)=a^{4}(3a^4+4)(3a^4-4)\)
9. \(108x^{8}-75x^{4}=3x^{4}(36x^{4}-25)=3x^{4}(6x^2+5)(6x^2-5)\)
10. \(2p^{6}+12p^{5}+18p^{4}=2p^{4}(p^2+6p+9)=2p^{4}(p+3)^2\)
11. \(3a^{5}-192a^{3}=3a^{3}(a^2-64)=3a^{3}(a+8)(a-8)\)
12. \(-98y^{4}+252y^{3}-162y^{2}=-2y^{2}(49y^{2}-126y+81)=-2y^{2}(7y-9)^2\)