Ontbinden in factoren (2)

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

1. \(-45q^{4}+5q^{2}\)
2. \(-128y^{7}-224y^{6}-98y^{5}\)
3. \(2a^{6}-2a^{4}\)
4. \(80p^{7}-120p^{5}+45p^{3}\)
5. \(216s^{6}+72s^{4}y+6s^{2}y^2\)
6. \(-108a^{16}+75a^{2}\)
7. \(6a^{6}-72a^{5}+216a^{4}\)
8. \(128q^{8}+96q^{6}+18q^{4}\)
9. \(-12p^{5}-12p^{4}-3p^{3}\)
10. \(-72a^{13}+120a^{8}y-50a^{3}y^2\)
11. \(-245a^{9}+210a^{6}-45a^{3}\)
12. \(96a^{9}+48a^{7}x+6a^{5}x^2\)

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

Verbetersleutel

1. \(-45q^{4}+5q^{2}=-5q^{2}(9q^{2}-1)=-5q^{2}(3q+1)(3q-1)\)
2. \(-128y^{7}-224y^{6}-98y^{5}=-2y^{5}(64y^{2}+112y+49)=-2y^{5}(8y+7)^2\)
3. \(2a^{6}-2a^{4}=2a^{4}(a^2-1)=2a^{4}(a+1)(a-1)\)
4. \(80p^{7}-120p^{5}+45p^{3}=5p^{3}(16p^{4}-24p^2+9)=5p^{3}(4p^2-3)^2\)
5. \(216s^{6}+72s^{4}y+6s^{2}y^2=6s^{2}(36s^{4}+12s^2y+y^2)=6s^{2}(6s^2+y)^2\)
6. \(-108a^{16}+75a^{2}=-3a^{2}(36a^{14}-25)=-3a^{2}(6a^7+5)(6a^7-5)\)
7. \(6a^{6}-72a^{5}+216a^{4}=6a^{4}(a^2-12a+36)=6a^{4}(a-6)^2\)
8. \(128q^{8}+96q^{6}+18q^{4}=2q^{4}(64q^{4}+48q^2+9)=2q^{4}(8q^2+3)^2\)
9. \(-12p^{5}-12p^{4}-3p^{3}=-3p^{3}(4p^{2}+4p+1)=-3p^{3}(2p+1)^2\)
10. \(-72a^{13}+120a^{8}y-50a^{3}y^2=-2a^{3}(36a^{10}-60a^5y+25y^2)=-2a^{3}(6a^5-5y)^2\)
11. \(-245a^{9}+210a^{6}-45a^{3}=-5a^{3}(49a^{6}-42a^3+9)=-5a^{3}(7a^3-3)^2\)
12. \(96a^{9}+48a^{7}x+6a^{5}x^2=6a^{5}(16a^{4}+8a^2x+x^2)=6a^{5}(4a^2+x)^2\)