Ontbinden in factoren (2)

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

1. \(27a^{13}+18a^{9}q+3a^{5}q^2\)
2. \(-98y^{11}-140y^{8}-50y^{5}\)
3. \(4s^{10}+4s^{7}+s^{4}\)
4. \(45y^{9}-150y^{7}+125y^{5}\)
5. \(-180a^{5}+125a^{3}\)
6. \(72s^{5}+120s^{4}+50s^{3}\)
7. \(-216b^{4}-72b^{3}-6b^{2}\)
8. \(-27y^{13}+75y^{5}\)
9. \(24x^{4}-6x^{2}\)
10. \(-6a^{7}+24a^{5}\)
11. \(-96q^{6}-240q^{5}-150q^{4}\)
12. \(-p^{6}+2p^{5}-p^{4}\)

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

Verbetersleutel

1. \(27a^{13}+18a^{9}q+3a^{5}q^2=3a^{5}(9a^{8}+6a^4q+q^2)=3a^{5}(3a^4+q)^2\)
2. \(-98y^{11}-140y^{8}-50y^{5}=-2y^{5}(49y^{6}+70y^3+25)=-2y^{5}(7y^3+5)^2\)
3. \(4s^{10}+4s^{7}+s^{4}=s^{4}(4s^{6}+4s^3+1)=s^{4}(2s^3+1)^2\)
4. \(45y^{9}-150y^{7}+125y^{5}=5y^{5}(9y^{4}-30y^2+25)=5y^{5}(3y^2-5)^2\)
5. \(-180a^{5}+125a^{3}=-5a^{3}(36a^{2}-25)=-5a^{3}(6a+5)(6a-5)\)
6. \(72s^{5}+120s^{4}+50s^{3}=2s^{3}(36s^{2}+60s+25)=2s^{3}(6s+5)^2\)
7. \(-216b^{4}-72b^{3}-6b^{2}=-6b^{2}(36b^{2}+12b+1)=-6b^{2}(6b+1)^2\)
8. \(-27y^{13}+75y^{5}=-3y^{5}(9y^{8}-25)=-3y^{5}(3y^4+5)(3y^4-5)\)
9. \(24x^{4}-6x^{2}=6x^{2}(4x^{2}-1)=6x^{2}(2x+1)(2x-1)\)
10. \(-6a^{7}+24a^{5}=-6a^{5}(a^2-4)=-6a^{5}(a+2)(a-2)\)
11. \(-96q^{6}-240q^{5}-150q^{4}=-6q^{4}(16q^{2}+40q+25)=-6q^{4}(4q+5)^2\)
12. \(-p^{6}+2p^{5}-p^{4}=-p^{4}(p^2-2p+1)=-p^{4}(p-1)^2\)