Ontbinden in factoren (2)

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

1. \(-24y^{21}+150y^{5}\)
2. \(-48x^{20}+27x^{4}\)
3. \(-245a^{12}+210a^{8}b-45a^{4}b^2\)
4. \(125b^{5}-450b^{4}+405b^{3}\)
5. \(3y^{6}-54y^{5}+243y^{4}\)
6. \(-12x^{8}+75x^{2}\)
7. \(2y^{4}-2y^{2}\)
8. \(-27q^{14}+90q^{9}-75q^{4}\)
9. \(-245s^{6}-210s^{5}-45s^{4}\)
10. \(-6q^{6}+6q^{4}\)
11. \(27a^{12}+36a^{8}+12a^{4}\)
12. \(245a^{4}-210a^{3}+45a^{2}\)

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

Verbetersleutel

1. \(-24y^{21}+150y^{5}=-6y^{5}(4y^{16}-25)=-6y^{5}(2y^8+5)(2y^8-5)\)
2. \(-48x^{20}+27x^{4}=-3x^{4}(16x^{16}-9)=-3x^{4}(4x^8+3)(4x^8-3)\)
3. \(-245a^{12}+210a^{8}b-45a^{4}b^2=-5a^{4}(49a^{8}-42a^4b+9b^2)=-5a^{4}(7a^4-3b)^2\)
4. \(125b^{5}-450b^{4}+405b^{3}=5b^{3}(25b^{2}-90b+81)=5b^{3}(5b-9)^2\)
5. \(3y^{6}-54y^{5}+243y^{4}=3y^{4}(y^2-18y+81)=3y^{4}(y-9)^2\)
6. \(-12x^{8}+75x^{2}=-3x^{2}(4x^{6}-25)=-3x^{2}(2x^3+5)(2x^3-5)\)
7. \(2y^{4}-2y^{2}=2y^{2}(y^2-1)=2y^{2}(y+1)(y-1)\)
8. \(-27q^{14}+90q^{9}-75q^{4}=-3q^{4}(9q^{10}-30q^5+25)=-3q^{4}(3q^5-5)^2\)
9. \(-245s^{6}-210s^{5}-45s^{4}=-5s^{4}(49s^{2}+42s+9)=-5s^{4}(7s+3)^2\)
10. \(-6q^{6}+6q^{4}=-6q^{4}(q^2-1)=-6q^{4}(q+1)(q-1)\)
11. \(27a^{12}+36a^{8}+12a^{4}=3a^{4}(9a^{8}+12a^4+4)=3a^{4}(3a^4+2)^2\)
12. \(245a^{4}-210a^{3}+45a^{2}=5a^{2}(49a^{2}-42a+9)=5a^{2}(7a-3)^2\)