Ontbinden in factoren (2)

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

1. \(18b^{9}-24b^{6}+8b^{3}\)
2. \(-64q^{13}+80q^{8}x-25q^{3}x^2\)
3. \(12a^{12}-27a^{4}\)
4. \(-p^{4}-14p^{3}-49p^{2}\)
5. \(125s^{7}-45s^{5}\)
6. \(108b^{18}-75b^{4}\)
7. \(-216a^{13}+360a^{9}q-150a^{5}q^2\)
8. \(50x^{6}-2x^{4}\)
9. \(-8p^{7}-24p^{5}q-18p^{3}q^2\)
10. \(12y^{6}-27y^{4}\)
11. \(-8b^{7}-72b^{6}-162b^{5}\)
12. \(-5b^{7}-10b^{6}-5b^{5}\)

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

Verbetersleutel

1. \(18b^{9}-24b^{6}+8b^{3}=2b^{3}(9b^{6}-12b^3+4)=2b^{3}(3b^3-2)^2\)
2. \(-64q^{13}+80q^{8}x-25q^{3}x^2=-q^{3}(64q^{10}-80q^5x+25x^2)=-q^{3}(8q^5-5x)^2\)
3. \(12a^{12}-27a^{4}=3a^{4}(4a^{8}-9)=3a^{4}(2a^4+3)(2a^4-3)\)
4. \(-p^{4}-14p^{3}-49p^{2}=-p^{2}(p^2+14p+49)=-p^{2}(p+7)^2\)
5. \(125s^{7}-45s^{5}=5s^{5}(25s^{2}-9)=5s^{5}(5s+3)(5s-3)\)
6. \(108b^{18}-75b^{4}=3b^{4}(36b^{14}-25)=3b^{4}(6b^7+5)(6b^7-5)\)
7. \(-216a^{13}+360a^{9}q-150a^{5}q^2=-6a^{5}(36a^{8}-60a^4q+25q^2)=-6a^{5}(6a^4-5q)^2\)
8. \(50x^{6}-2x^{4}=2x^{4}(25x^{2}-1)=2x^{4}(5x+1)(5x-1)\)
9. \(-8p^{7}-24p^{5}q-18p^{3}q^2=-2p^{3}(4p^{4}+12p^2q+9q^2)=-2p^{3}(2p^2+3q)^2\)
10. \(12y^{6}-27y^{4}=3y^{4}(4y^{2}-9)=3y^{4}(2y+3)(2y-3)\)
11. \(-8b^{7}-72b^{6}-162b^{5}=-2b^{5}(4b^{2}+36b+81)=-2b^{5}(2b+9)^2\)
12. \(-5b^{7}-10b^{6}-5b^{5}=-5b^{5}(b^2+2b+1)=-5b^{5}(b+1)^2\)