Ontbinden in factoren (2)

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

1. \(-8b^{5}+98b^{3}\)
2. \(b^{6}-16b^{4}\)
3. \(-2x^{7}+2x^{5}\)
4. \(6x^{4}-216x^{2}\)
5. \(-3s^{6}+48s^{5}-192s^{4}\)
6. \(36a^{4}-a^{2}\)
7. \(245p^{13}+70p^{8}+5p^{3}\)
8. \(216b^{9}-360b^{7}s+150b^{5}s^2\)
9. \(125s^{13}-180s^{3}\)
10. \(320a^{8}-560a^{6}+245a^{4}\)
11. \(32p^{7}-2p^{5}\)
12. \(-54q^{5}+6q^{3}\)

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

Verbetersleutel

1. \(-8b^{5}+98b^{3}=-2b^{3}(4b^{2}-49)=-2b^{3}(2b+7)(2b-7)\)
2. \(b^{6}-16b^{4}=b^{4}(b^2-16)=b^{4}(b+4)(b-4)\)
3. \(-2x^{7}+2x^{5}=-2x^{5}(x^2-1)=-2x^{5}(x-1)(x+1)\)
4. \(6x^{4}-216x^{2}=6x^{2}(x^2-36)=6x^{2}(x+6)(x-6)\)
5. \(-3s^{6}+48s^{5}-192s^{4}=-3s^{4}(s^2-16s+64)=-3s^{4}(s-8)^2\)
6. \(36a^{4}-a^{2}=a^{2}(36a^{2}-1)=a^{2}(6a+1)(6a-1)\)
7. \(245p^{13}+70p^{8}+5p^{3}=5p^{3}(49p^{10}+14p^5+1)=5p^{3}(7p^5+1)^2\)
8. \(216b^{9}-360b^{7}s+150b^{5}s^2=6b^{5}(36b^{4}-60b^2s+25s^2)=6b^{5}(6b^2-5s)^2\)
9. \(125s^{13}-180s^{3}=5s^{3}(25s^{10}-36)=5s^{3}(5s^5+6)(5s^5-6)\)
10. \(320a^{8}-560a^{6}+245a^{4}=5a^{4}(64a^{4}-112a^2+49)=5a^{4}(8a^2-7)^2\)
11. \(32p^{7}-2p^{5}=2p^{5}(16p^{2}-1)=2p^{5}(4p+1)(4p-1)\)
12. \(-54q^{5}+6q^{3}=-6q^{3}(9q^{2}-1)=-6q^{3}(3q+1)(3q-1)\)