Ontbinden in factoren (2)

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

1. \(-9b^{9}-6b^{7}-b^{5}\)
2. \(-3b^{6}+75b^{4}\)
3. \(6y^{7}-384y^{5}\)
4. \(-5y^{5}-60y^{4}-180y^{3}\)
5. \(-32b^{14}+48b^{9}-18b^{4}\)
6. \(-8y^{20}+98y^{4}\)
7. \(-96a^{5}+336a^{4}-294a^{3}\)
8. \(-6p^{6}+150p^{4}\)
9. \(8a^{13}-18a^{5}\)
10. \(-128b^{6}-32b^{5}-2b^{4}\)
11. \(-27b^{15}+3b^{3}\)
12. \(12x^{8}-147x^{4}\)

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

Verbetersleutel

1. \(-9b^{9}-6b^{7}-b^{5}=-b^{5}(9b^{4}+6b^2+1)=-b^{5}(3b^2+1)^2\)
2. \(-3b^{6}+75b^{4}=-3b^{4}(b^2-25)=-3b^{4}(b+5)(b-5)\)
3. \(6y^{7}-384y^{5}=6y^{5}(y^2-64)=6y^{5}(y-8)(y+8)\)
4. \(-5y^{5}-60y^{4}-180y^{3}=-5y^{3}(y^2+12y+36)=-5y^{3}(y+6)^2\)
5. \(-32b^{14}+48b^{9}-18b^{4}=-2b^{4}(16b^{10}-24b^5+9)=-2b^{4}(4b^5-3)^2\)
6. \(-8y^{20}+98y^{4}=-2y^{4}(4y^{16}-49)=-2y^{4}(2y^8+7)(2y^8-7)\)
7. \(-96a^{5}+336a^{4}-294a^{3}=-6a^{3}(16a^{2}-56a+49)=-6a^{3}(4a-7)^2\)
8. \(-6p^{6}+150p^{4}=-6p^{4}(p^2-25)=-6p^{4}(p-5)(p+5)\)
9. \(8a^{13}-18a^{5}=2a^{5}(4a^{8}-9)=2a^{5}(2a^4+3)(2a^4-3)\)
10. \(-128b^{6}-32b^{5}-2b^{4}=-2b^{4}(64b^{2}+16b+1)=-2b^{4}(8b+1)^2\)
11. \(-27b^{15}+3b^{3}=-3b^{3}(9b^{12}-1)=-3b^{3}(3b^6+1)(3b^6-1)\)
12. \(12x^{8}-147x^{4}=3x^{4}(4x^{4}-49)=3x^{4}(2x^2+7)(2x^2-7)\)