Ontbinden in factoren (2)

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

1. \(128p^{14}+96p^{9}+18p^{4}\)
2. \(-75q^{5}+27q^{3}\)
3. \(-125y^{7}+245y^{5}\)
4. \(q^{5}+14q^{4}+49q^{3}\)
5. \(-98y^{7}+168y^{6}-72y^{5}\)
6. \(48a^{13}-168a^{9}p+147a^{5}p^2\)
7. \(108s^{10}+180s^{6}+75s^{2}\)
8. \(-96q^{19}+6q^{3}\)
9. \(-6a^{4}+150a^{2}\)
10. \(20a^{14}+20a^{9}y+5a^{4}y^2\)
11. \(-150q^{11}+6q^{3}\)
12. \(-a^{6}+6a^{5}-9a^{4}\)

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

Verbetersleutel

1. \(128p^{14}+96p^{9}+18p^{4}=2p^{4}(64p^{10}+48p^5+9)=2p^{4}(8p^5+3)^2\)
2. \(-75q^{5}+27q^{3}=-3q^{3}(25q^{2}-9)=-3q^{3}(5q+3)(5q-3)\)
3. \(-125y^{7}+245y^{5}=-5y^{5}(25y^{2}-49)=-5y^{5}(5y+7)(5y-7)\)
4. \(q^{5}+14q^{4}+49q^{3}=q^{3}(q^2+14q+49)=q^{3}(q+7)^2\)
5. \(-98y^{7}+168y^{6}-72y^{5}=-2y^{5}(49y^{2}-84y+36)=-2y^{5}(7y-6)^2\)
6. \(48a^{13}-168a^{9}p+147a^{5}p^2=3a^{5}(16a^{8}-56a^4p+49p^2)=3a^{5}(4a^4-7p)^2\)
7. \(108s^{10}+180s^{6}+75s^{2}=3s^{2}(36s^{8}+60s^4+25)=3s^{2}(6s^4+5)^2\)
8. \(-96q^{19}+6q^{3}=-6q^{3}(16q^{16}-1)=-6q^{3}(4q^8+1)(4q^8-1)\)
9. \(-6a^{4}+150a^{2}=-6a^{2}(a^2-25)=-6a^{2}(a-5)(a+5)\)
10. \(20a^{14}+20a^{9}y+5a^{4}y^2=5a^{4}(4a^{10}+4a^5y+y^2)=5a^{4}(2a^5+y)^2\)
11. \(-150q^{11}+6q^{3}=-6q^{3}(25q^{8}-1)=-6q^{3}(5q^4+1)(5q^4-1)\)
12. \(-a^{6}+6a^{5}-9a^{4}=-a^{4}(a^2-6a+9)=-a^{4}(a-3)^2\)