Ontbinden in factoren (2)

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

1. \(245p^{14}-420p^{9}q+180p^{4}q^2\)
2. \(9p^{12}-12p^{8}y+4p^{4}y^2\)
3. \(-45p^{11}+5p^{5}\)
4. \(-245s^{6}+630s^{5}-405s^{4}\)
5. \(-36a^{10}-12a^{6}s-a^{2}s^2\)
6. \(-125q^{4}+45q^{2}\)
7. \(-75x^{18}+147x^{4}\)
8. \(25s^{9}-36s^{3}\)
9. \(150p^{12}-240p^{8}+96p^{4}\)
10. \(-2b^{6}-24b^{5}-72b^{4}\)
11. \(-72y^{7}+98y^{5}\)
12. \(25p^{6}-36p^{4}\)

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

Verbetersleutel

1. \(245p^{14}-420p^{9}q+180p^{4}q^2=5p^{4}(49p^{10}-84p^5q+36q^2)=5p^{4}(7p^5-6q)^2\)
2. \(9p^{12}-12p^{8}y+4p^{4}y^2=p^{4}(9p^{8}-12p^4y+4y^2)=p^{4}(3p^4-2y)^2\)
3. \(-45p^{11}+5p^{5}=-5p^{5}(9p^{6}-1)=-5p^{5}(3p^3+1)(3p^3-1)\)
4. \(-245s^{6}+630s^{5}-405s^{4}=-5s^{4}(49s^{2}-126s+81)=-5s^{4}(7s-9)^2\)
5. \(-36a^{10}-12a^{6}s-a^{2}s^2=-a^{2}(36a^{8}+12a^4s+s^2)=-a^{2}(6a^4+s)^2\)
6. \(-125q^{4}+45q^{2}=-5q^{2}(25q^{2}-9)=-5q^{2}(5q+3)(5q-3)\)
7. \(-75x^{18}+147x^{4}=-3x^{4}(25x^{14}-49)=-3x^{4}(5x^7+7)(5x^7-7)\)
8. \(25s^{9}-36s^{3}=s^{3}(25s^{6}-36)=s^{3}(5s^3+6)(5s^3-6)\)
9. \(150p^{12}-240p^{8}+96p^{4}=6p^{4}(25p^{8}-40p^4+16)=6p^{4}(5p^4-4)^2\)
10. \(-2b^{6}-24b^{5}-72b^{4}=-2b^{4}(b^2+12b+36)=-2b^{4}(b+6)^2\)
11. \(-72y^{7}+98y^{5}=-2y^{5}(36y^{2}-49)=-2y^{5}(6y+7)(6y-7)\)
12. \(25p^{6}-36p^{4}=p^{4}(25p^{2}-36)=p^{4}(5p+6)(5p-6)\)