Ontbinden in factoren (2)

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

1. \(108x^{4}-3x^{2}\)
2. \(-3s^{6}+48s^{4}\)
3. \(180s^{15}-125s^{5}\)
4. \(48b^{13}-72b^{8}+27b^{3}\)
5. \(-245p^{14}+420p^{9}x-180p^{4}x^2\)
6. \(18q^{4}-60q^{3}+50q^{2}\)
7. \(-125a^{7}+200a^{6}-80a^{5}\)
8. \(6p^{5}+60p^{4}+150p^{3}\)
9. \(-16x^{13}-24x^{8}y-9x^{3}y^2\)
10. \(-150y^{10}+24y^{2}\)
11. \(5x^{4}-5x^{2}\)
12. \(20q^{5}+20q^{4}+5q^{3}\)

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

Verbetersleutel

1. \(108x^{4}-3x^{2}=3x^{2}(36x^{2}-1)=3x^{2}(6x+1)(6x-1)\)
2. \(-3s^{6}+48s^{4}=-3s^{4}(s^2-16)=-3s^{4}(s+4)(s-4)\)
3. \(180s^{15}-125s^{5}=5s^{5}(36s^{10}-25)=5s^{5}(6s^5+5)(6s^5-5)\)
4. \(48b^{13}-72b^{8}+27b^{3}=3b^{3}(16b^{10}-24b^5+9)=3b^{3}(4b^5-3)^2\)
5. \(-245p^{14}+420p^{9}x-180p^{4}x^2=-5p^{4}(49p^{10}-84p^5x+36x^2)=-5p^{4}(7p^5-6x)^2\)
6. \(18q^{4}-60q^{3}+50q^{2}=2q^{2}(9q^{2}-30q+25)=2q^{2}(3q-5)^2\)
7. \(-125a^{7}+200a^{6}-80a^{5}=-5a^{5}(25a^{2}-40a+16)=-5a^{5}(5a-4)^2\)
8. \(6p^{5}+60p^{4}+150p^{3}=6p^{3}(p^2+10p+25)=6p^{3}(p+5)^2\)
9. \(-16x^{13}-24x^{8}y-9x^{3}y^2=-x^{3}(16x^{10}+24x^5y+9y^2)=-x^{3}(4x^5+3y)^2\)
10. \(-150y^{10}+24y^{2}=-6y^{2}(25y^{8}-4)=-6y^{2}(5y^4+2)(5y^4-2)\)
11. \(5x^{4}-5x^{2}=5x^{2}(x^2-1)=5x^{2}(x+1)(x-1)\)
12. \(20q^{5}+20q^{4}+5q^{3}=5q^{3}(4q^{2}+4q+1)=5q^{3}(2q+1)^2\)