Ontbinden in factoren (2)

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

1. \(12b^{5}-75b^{3}\)
2. \(384a^{7}+288a^{5}+54a^{3}\)
3. \(125a^{7}-180a^{5}\)
4. \(16a^{6}+40a^{5}+25a^{4}\)
5. \(-32q^{5}-16q^{4}-2q^{3}\)
6. \(-45x^{6}+20x^{4}\)
7. \(16y^{6}-49y^{4}\)
8. \(-20s^{5}-60s^{4}-45s^{3}\)
9. \(-3y^{4}+75y^{2}\)
10. \(-8b^{9}-8b^{7}-2b^{5}\)
11. \(48b^{5}-147b^{3}\)
12. \(4p^{12}-9p^{2}\)

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

Verbetersleutel

1. \(12b^{5}-75b^{3}=3b^{3}(4b^{2}-25)=3b^{3}(2b+5)(2b-5)\)
2. \(384a^{7}+288a^{5}+54a^{3}=6a^{3}(64a^{4}+48a^2+9)=6a^{3}(8a^2+3)^2\)
3. \(125a^{7}-180a^{5}=5a^{5}(25a^{2}-36)=5a^{5}(5a+6)(5a-6)\)
4. \(16a^{6}+40a^{5}+25a^{4}=a^{4}(16a^{2}+40a+25)=a^{4}(4a+5)^2\)
5. \(-32q^{5}-16q^{4}-2q^{3}=-2q^{3}(16q^{2}+8q+1)=-2q^{3}(4q+1)^2\)
6. \(-45x^{6}+20x^{4}=-5x^{4}(9x^{2}-4)=-5x^{4}(3x+2)(3x-2)\)
7. \(16y^{6}-49y^{4}=y^{4}(16y^{2}-49)=y^{4}(4y+7)(4y-7)\)
8. \(-20s^{5}-60s^{4}-45s^{3}=-5s^{3}(4s^{2}+12s+9)=-5s^{3}(2s+3)^2\)
9. \(-3y^{4}+75y^{2}=-3y^{2}(y^2-25)=-3y^{2}(y+5)(y-5)\)
10. \(-8b^{9}-8b^{7}-2b^{5}=-2b^{5}(4b^{4}+4b^2+1)=-2b^{5}(2b^2+1)^2\)
11. \(48b^{5}-147b^{3}=3b^{3}(16b^{2}-49)=3b^{3}(4b+7)(4b-7)\)
12. \(4p^{12}-9p^{2}=p^{2}(4p^{10}-9)=p^{2}(2p^5+3)(2p^5-3)\)