Ontbinden in factoren (2)

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

1. \(32b^{7}-48b^{6}+18b^{5}\)
2. \(8s^{7}-18s^{5}\)
3. \(-y^{4}-6y^{3}-9y^{2}\)
4. \(108a^{9}+180a^{6}p+75a^{3}p^2\)
5. \(3b^{5}-192b^{3}\)
6. \(24q^{7}+24q^{6}+6q^{5}\)
7. \(16q^{12}+8q^{8}+q^{4}\)
8. \(5p^{6}-125p^{4}\)
9. \(36q^{13}-25q^{3}\)
10. \(-48p^{4}-120p^{3}-75p^{2}\)
11. \(-216p^{14}-72p^{9}x-6p^{4}x^2\)
12. \(245b^{10}+210b^{6}+45b^{2}\)

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

Verbetersleutel

1. \(32b^{7}-48b^{6}+18b^{5}=2b^{5}(16b^{2}-24b+9)=2b^{5}(4b-3)^2\)
2. \(8s^{7}-18s^{5}=2s^{5}(4s^{2}-9)=2s^{5}(2s+3)(2s-3)\)
3. \(-y^{4}-6y^{3}-9y^{2}=-y^{2}(y^2+6y+9)=-y^{2}(y+3)^2\)
4. \(108a^{9}+180a^{6}p+75a^{3}p^2=3a^{3}(36a^{6}+60a^3p+25p^2)=3a^{3}(6a^3+5p)^2\)
5. \(3b^{5}-192b^{3}=3b^{3}(b^2-64)=3b^{3}(b+8)(b-8)\)
6. \(24q^{7}+24q^{6}+6q^{5}=6q^{5}(4q^{2}+4q+1)=6q^{5}(2q+1)^2\)
7. \(16q^{12}+8q^{8}+q^{4}=q^{4}(16q^{8}+8q^4+1)=q^{4}(4q^4+1)^2\)
8. \(5p^{6}-125p^{4}=5p^{4}(p^2-25)=5p^{4}(p-5)(p+5)\)
9. \(36q^{13}-25q^{3}=q^{3}(36q^{10}-25)=q^{3}(6q^5+5)(6q^5-5)\)
10. \(-48p^{4}-120p^{3}-75p^{2}=-3p^{2}(16p^{2}+40p+25)=-3p^{2}(4p+5)^2\)
11. \(-216p^{14}-72p^{9}x-6p^{4}x^2=-6p^{4}(36p^{10}+12p^5x+x^2)=-6p^{4}(6p^5+x)^2\)
12. \(245b^{10}+210b^{6}+45b^{2}=5b^{2}(49b^{8}+42b^4+9)=5b^{2}(7b^4+3)^2\)