Ontbinden in factoren (2)

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

1. \(125b^{6}+350b^{5}+245b^{4}\)
2. \(a^{7}-18a^{6}+81a^{5}\)
3. \(16b^{4}-9b^{2}\)
4. \(y^{6}-16y^{4}\)
5. \(24q^{18}-54q^{4}\)
6. \(6a^{4}+72a^{3}+216a^{2}\)
7. \(-25x^{8}+36x^{2}\)
8. \(-5a^{7}+125a^{5}\)
9. \(-32a^{11}-80a^{8}y-50a^{5}y^2\)
10. \(-4b^{10}-4b^{6}p-b^{2}p^2\)
11. \(-245b^{5}+420b^{4}-180b^{3}\)
12. \(80b^{7}+200b^{5}+125b^{3}\)

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

Verbetersleutel

1. \(125b^{6}+350b^{5}+245b^{4}=5b^{4}(25b^{2}+70b+49)=5b^{4}(5b+7)^2\)
2. \(a^{7}-18a^{6}+81a^{5}=a^{5}(a^2-18a+81)=a^{5}(a-9)^2\)
3. \(16b^{4}-9b^{2}=b^{2}(16b^{2}-9)=b^{2}(4b+3)(4b-3)\)
4. \(y^{6}-16y^{4}=y^{4}(y^2-16)=y^{4}(y+4)(y-4)\)
5. \(24q^{18}-54q^{4}=6q^{4}(4q^{14}-9)=6q^{4}(2q^7+3)(2q^7-3)\)
6. \(6a^{4}+72a^{3}+216a^{2}=6a^{2}(a^2+12a+36)=6a^{2}(a+6)^2\)
7. \(-25x^{8}+36x^{2}=-x^{2}(25x^{6}-36)=-x^{2}(5x^3+6)(5x^3-6)\)
8. \(-5a^{7}+125a^{5}=-5a^{5}(a^2-25)=-5a^{5}(a+5)(a-5)\)
9. \(-32a^{11}-80a^{8}y-50a^{5}y^2=-2a^{5}(16a^{6}+40a^3y+25y^2)=-2a^{5}(4a^3+5y)^2\)
10. \(-4b^{10}-4b^{6}p-b^{2}p^2=-b^{2}(4b^{8}+4b^4p+p^2)=-b^{2}(2b^4+p)^2\)
11. \(-245b^{5}+420b^{4}-180b^{3}=-5b^{3}(49b^{2}-84b+36)=-5b^{3}(7b-6)^2\)
12. \(80b^{7}+200b^{5}+125b^{3}=5b^{3}(16b^{4}+40b^2+25)=5b^{3}(4b^2+5)^2\)