Ontbinden in factoren (2)

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

1. \(-8p^{13}+18p^{5}\)
2. \(50p^{6}-98p^{4}\)
3. \(6a^{5}-108a^{4}+486a^{3}\)
4. \(-72p^{8}-24p^{5}x-2p^{2}x^2\)
5. \(-36b^{8}-12b^{5}x-b^{2}x^2\)
6. \(54a^{16}-96a^{2}\)
7. \(108y^{12}-3y^{4}\)
8. \(98a^{6}-168a^{4}+72a^{2}\)
9. \(3p^{6}-75p^{4}\)
10. \(3s^{4}-48s^{3}+192s^{2}\)
11. \(3a^{4}+30a^{3}+75a^{2}\)
12. \(-3b^{7}+192b^{5}\)

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

Verbetersleutel

1. \(-8p^{13}+18p^{5}=-2p^{5}(4p^{8}-9)=-2p^{5}(2p^4+3)(2p^4-3)\)
2. \(50p^{6}-98p^{4}=2p^{4}(25p^{2}-49)=2p^{4}(5p+7)(5p-7)\)
3. \(6a^{5}-108a^{4}+486a^{3}=6a^{3}(a^2-18a+81)=6a^{3}(a-9)^2\)
4. \(-72p^{8}-24p^{5}x-2p^{2}x^2=-2p^{2}(36p^{6}+12p^3x+x^2)=-2p^{2}(6p^3+x)^2\)
5. \(-36b^{8}-12b^{5}x-b^{2}x^2=-b^{2}(36b^{6}+12b^3x+x^2)=-b^{2}(6b^3+x)^2\)
6. \(54a^{16}-96a^{2}=6a^{2}(9a^{14}-16)=6a^{2}(3a^7+4)(3a^7-4)\)
7. \(108y^{12}-3y^{4}=3y^{4}(36y^{8}-1)=3y^{4}(6y^4+1)(6y^4-1)\)
8. \(98a^{6}-168a^{4}+72a^{2}=2a^{2}(49a^{4}-84a^2+36)=2a^{2}(7a^2-6)^2\)
9. \(3p^{6}-75p^{4}=3p^{4}(p^2-25)=3p^{4}(p+5)(p-5)\)
10. \(3s^{4}-48s^{3}+192s^{2}=3s^{2}(s^2-16s+64)=3s^{2}(s-8)^2\)
11. \(3a^{4}+30a^{3}+75a^{2}=3a^{2}(a^2+10a+25)=3a^{2}(a+5)^2\)
12. \(-3b^{7}+192b^{5}=-3b^{5}(b^2-64)=-3b^{5}(b-8)(b+8)\)