Ontbinden in factoren (2)

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

1. \(-9x^{6}+12x^{4}-4x^{2}\)
2. \(-16y^{8}-40y^{6}-25y^{4}\)
3. \(-108a^{10}-180a^{6}y-75a^{2}y^2\)
4. \(45p^{11}-80p^{3}\)
5. \(12q^{7}+12q^{6}+3q^{5}\)
6. \(-49p^{6}+28p^{5}-4p^{4}\)
7. \(384p^{6}-480p^{4}s+150p^{2}s^2\)
8. \(16b^{7}+8b^{6}+b^{5}\)
9. \(-4s^{13}+49s^{3}\)
10. \(125a^{6}-80a^{4}\)
11. \(-5p^{4}+80p^{2}\)
12. \(45p^{12}-150p^{7}+125p^{2}\)

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

Verbetersleutel

1. \(-9x^{6}+12x^{4}-4x^{2}=-x^{2}(9x^{4}-12x^2+4)=-x^{2}(3x^2-2)^2\)
2. \(-16y^{8}-40y^{6}-25y^{4}=-y^{4}(16y^{4}+40y^2+25)=-y^{4}(4y^2+5)^2\)
3. \(-108a^{10}-180a^{6}y-75a^{2}y^2=-3a^{2}(36a^{8}+60a^4y+25y^2)=-3a^{2}(6a^4+5y)^2\)
4. \(45p^{11}-80p^{3}=5p^{3}(9p^{8}-16)=5p^{3}(3p^4+4)(3p^4-4)\)
5. \(12q^{7}+12q^{6}+3q^{5}=3q^{5}(4q^{2}+4q+1)=3q^{5}(2q+1)^2\)
6. \(-49p^{6}+28p^{5}-4p^{4}=-p^{4}(49p^{2}-28p+4)=-p^{4}(7p-2)^2\)
7. \(384p^{6}-480p^{4}s+150p^{2}s^2=6p^{2}(64p^{4}-80p^2s+25s^2)=6p^{2}(8p^2-5s)^2\)
8. \(16b^{7}+8b^{6}+b^{5}=b^{5}(16b^{2}+8b+1)=b^{5}(4b+1)^2\)
9. \(-4s^{13}+49s^{3}=-s^{3}(4s^{10}-49)=-s^{3}(2s^5+7)(2s^5-7)\)
10. \(125a^{6}-80a^{4}=5a^{4}(25a^{2}-16)=5a^{4}(5a+4)(5a-4)\)
11. \(-5p^{4}+80p^{2}=-5p^{2}(p^2-16)=-5p^{2}(p-4)(p+4)\)
12. \(45p^{12}-150p^{7}+125p^{2}=5p^{2}(9p^{10}-30p^5+25)=5p^{2}(3p^5-5)^2\)