Ontbinden in factoren (2)

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

1. \(180s^{8}+60s^{6}+5s^{4}\)
2. \(24p^{8}+24p^{6}+6p^{4}\)
3. \(-125y^{14}+5y^{4}\)
4. \(-20a^{12}-20a^{7}p-5a^{2}p^2\)
5. \(125p^{4}-180p^{2}\)
6. \(-36a^{6}+25a^{4}\)
7. \(-50p^{11}+80p^{8}s-32p^{5}s^2\)
8. \(108y^{5}-75y^{3}\)
9. \(-96b^{9}+336b^{7}p-294b^{5}p^2\)
10. \(-45q^{12}-30q^{8}x-5q^{4}x^2\)
11. \(-5b^{4}-50b^{3}-125b^{2}\)
12. \(98p^{11}+28p^{8}q+2p^{5}q^2\)

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

Verbetersleutel

1. \(180s^{8}+60s^{6}+5s^{4}=5s^{4}(36s^{4}+12s^2+1)=5s^{4}(6s^2+1)^2\)
2. \(24p^{8}+24p^{6}+6p^{4}=6p^{4}(4p^{4}+4p^2+1)=6p^{4}(2p^2+1)^2\)
3. \(-125y^{14}+5y^{4}=-5y^{4}(25y^{10}-1)=-5y^{4}(5y^5+1)(5y^5-1)\)
4. \(-20a^{12}-20a^{7}p-5a^{2}p^2=-5a^{2}(4a^{10}+4a^5p+p^2)=-5a^{2}(2a^5+p)^2\)
5. \(125p^{4}-180p^{2}=5p^{2}(25p^{2}-36)=5p^{2}(5p+6)(5p-6)\)
6. \(-36a^{6}+25a^{4}=-a^{4}(36a^{2}-25)=-a^{4}(6a+5)(6a-5)\)
7. \(-50p^{11}+80p^{8}s-32p^{5}s^2=-2p^{5}(25p^{6}-40p^3s+16s^2)=-2p^{5}(5p^3-4s)^2\)
8. \(108y^{5}-75y^{3}=3y^{3}(36y^{2}-25)=3y^{3}(6y+5)(6y-5)\)
9. \(-96b^{9}+336b^{7}p-294b^{5}p^2=-6b^{5}(16b^{4}-56b^2p+49p^2)=-6b^{5}(4b^2-7p)^2\)
10. \(-45q^{12}-30q^{8}x-5q^{4}x^2=-5q^{4}(9q^{8}+6q^4x+x^2)=-5q^{4}(3q^4+x)^2\)
11. \(-5b^{4}-50b^{3}-125b^{2}=-5b^{2}(b^2+10b+25)=-5b^{2}(b+5)^2\)
12. \(98p^{11}+28p^{8}q+2p^{5}q^2=2p^{5}(49p^{6}+14p^3q+q^2)=2p^{5}(7p^3+q)^2\)