Ontbinden in factoren (2)

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

1. \(-9y^{16}+16y^{4}\)
2. \(-3x^{5}+3x^{3}\)
3. \(-320a^{12}-80a^{8}-5a^{4}\)
4. \(80a^{10}+40a^{6}+5a^{2}\)
5. \(-96a^{11}+6a^{5}\)
6. \(-54a^{13}+180a^{8}y-150a^{3}y^2\)
7. \(150a^{5}-54a^{3}\)
8. \(-54s^{5}+96s^{3}\)
9. \(20a^{4}-125a^{2}\)
10. \(32a^{18}-50a^{2}\)
11. \(6b^{7}+84b^{6}+294b^{5}\)
12. \(-384q^{8}-288q^{5}-54q^{2}\)

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

Verbetersleutel

1. \(-9y^{16}+16y^{4}=-y^{4}(9y^{12}-16)=-y^{4}(3y^6+4)(3y^6-4)\)
2. \(-3x^{5}+3x^{3}=-3x^{3}(x^2-1)=-3x^{3}(x+1)(x-1)\)
3. \(-320a^{12}-80a^{8}-5a^{4}=-5a^{4}(64a^{8}+16a^4+1)=-5a^{4}(8a^4+1)^2\)
4. \(80a^{10}+40a^{6}+5a^{2}=5a^{2}(16a^{8}+8a^4+1)=5a^{2}(4a^4+1)^2\)
5. \(-96a^{11}+6a^{5}=-6a^{5}(16a^{6}-1)=-6a^{5}(4a^3+1)(4a^3-1)\)
6. \(-54a^{13}+180a^{8}y-150a^{3}y^2=-6a^{3}(9a^{10}-30a^5y+25y^2)=-6a^{3}(3a^5-5y)^2\)
7. \(150a^{5}-54a^{3}=6a^{3}(25a^{2}-9)=6a^{3}(5a+3)(5a-3)\)
8. \(-54s^{5}+96s^{3}=-6s^{3}(9s^{2}-16)=-6s^{3}(3s+4)(3s-4)\)
9. \(20a^{4}-125a^{2}=5a^{2}(4a^{2}-25)=5a^{2}(2a+5)(2a-5)\)
10. \(32a^{18}-50a^{2}=2a^{2}(16a^{16}-25)=2a^{2}(4a^8+5)(4a^8-5)\)
11. \(6b^{7}+84b^{6}+294b^{5}=6b^{5}(b^2+14b+49)=6b^{5}(b+7)^2\)
12. \(-384q^{8}-288q^{5}-54q^{2}=-6q^{2}(64q^{6}+48q^3+9)=-6q^{2}(8q^3+3)^2\)