Ontbinden in factoren (2)

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

1. \(24a^{9}+24a^{7}+6a^{5}\)
2. \(75q^{21}-3q^{5}\)
3. \(-18y^{20}+32y^{4}\)
4. \(80s^{4}-245s^{2}\)
5. \(-80q^{7}-40q^{6}-5q^{5}\)
6. \(-24p^{9}+294p^{3}\)
7. \(-216y^{5}+360y^{4}-150y^{3}\)
8. \(-y^{5}+49y^{3}\)
9. \(12s^{4}+12s^{3}+3s^{2}\)
10. \(-12p^{6}+3p^{4}\)
11. \(-245q^{14}-280q^{9}s-80q^{4}s^2\)
12. \(-125b^{11}-50b^{7}-5b^{3}\)

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

Verbetersleutel

1. \(24a^{9}+24a^{7}+6a^{5}=6a^{5}(4a^{4}+4a^2+1)=6a^{5}(2a^2+1)^2\)
2. \(75q^{21}-3q^{5}=3q^{5}(25q^{16}-1)=3q^{5}(5q^8+1)(5q^8-1)\)
3. \(-18y^{20}+32y^{4}=-2y^{4}(9y^{16}-16)=-2y^{4}(3y^8+4)(3y^8-4)\)
4. \(80s^{4}-245s^{2}=5s^{2}(16s^{2}-49)=5s^{2}(4s+7)(4s-7)\)
5. \(-80q^{7}-40q^{6}-5q^{5}=-5q^{5}(16q^{2}+8q+1)=-5q^{5}(4q+1)^2\)
6. \(-24p^{9}+294p^{3}=-6p^{3}(4p^{6}-49)=-6p^{3}(2p^3+7)(2p^3-7)\)
7. \(-216y^{5}+360y^{4}-150y^{3}=-6y^{3}(36y^{2}-60y+25)=-6y^{3}(6y-5)^2\)
8. \(-y^{5}+49y^{3}=-y^{3}(y^2-49)=-y^{3}(y+7)(y-7)\)
9. \(12s^{4}+12s^{3}+3s^{2}=3s^{2}(4s^{2}+4s+1)=3s^{2}(2s+1)^2\)
10. \(-12p^{6}+3p^{4}=-3p^{4}(4p^{2}-1)=-3p^{4}(2p+1)(2p-1)\)
11. \(-245q^{14}-280q^{9}s-80q^{4}s^2=-5q^{4}(49q^{10}+56q^5s+16s^2)=-5q^{4}(7q^5+4s)^2\)
12. \(-125b^{11}-50b^{7}-5b^{3}=-5b^{3}(25b^{8}+10b^4+1)=-5b^{3}(5b^4+1)^2\)