Ontbinden in factoren (2)

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

1. \(-216q^{12}-72q^{7}-6q^{2}\)
2. \(72a^{12}+120a^{7}p+50a^{2}p^2\)
3. \(180q^{12}+60q^{7}x+5q^{2}x^2\)
4. \(25y^{8}+60y^{6}+36y^{4}\)
5. \(20a^{12}+20a^{7}b+5a^{2}b^2\)
6. \(80p^{15}-120p^{10}q+45p^{5}q^2\)
7. \(25y^{6}+60y^{5}+36y^{4}\)
8. \(45y^{5}-245y^{3}\)
9. \(-54a^{18}+294a^{4}\)
10. \(-50a^{11}+40a^{8}b-8a^{5}b^2\)
11. \(-4s^{8}+s^{4}\)
12. \(-p^{4}+64p^{2}\)

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

Verbetersleutel

1. \(-216q^{12}-72q^{7}-6q^{2}=-6q^{2}(36q^{10}+12q^5+1)=-6q^{2}(6q^5+1)^2\)
2. \(72a^{12}+120a^{7}p+50a^{2}p^2=2a^{2}(36a^{10}+60a^5p+25p^2)=2a^{2}(6a^5+5p)^2\)
3. \(180q^{12}+60q^{7}x+5q^{2}x^2=5q^{2}(36q^{10}+12q^5x+x^2)=5q^{2}(6q^5+x)^2\)
4. \(25y^{8}+60y^{6}+36y^{4}=y^{4}(25y^{4}+60y^2+36)=y^{4}(5y^2+6)^2\)
5. \(20a^{12}+20a^{7}b+5a^{2}b^2=5a^{2}(4a^{10}+4a^5b+b^2)=5a^{2}(2a^5+b)^2\)
6. \(80p^{15}-120p^{10}q+45p^{5}q^2=5p^{5}(16p^{10}-24p^5q+9q^2)=5p^{5}(4p^5-3q)^2\)
7. \(25y^{6}+60y^{5}+36y^{4}=y^{4}(25y^{2}+60y+36)=y^{4}(5y+6)^2\)
8. \(45y^{5}-245y^{3}=5y^{3}(9y^{2}-49)=5y^{3}(3y+7)(3y-7)\)
9. \(-54a^{18}+294a^{4}=-6a^{4}(9a^{14}-49)=-6a^{4}(3a^7+7)(3a^7-7)\)
10. \(-50a^{11}+40a^{8}b-8a^{5}b^2=-2a^{5}(25a^{6}-20a^3b+4b^2)=-2a^{5}(5a^3-2b)^2\)
11. \(-4s^{8}+s^{4}=-s^{4}(4s^{4}-1)=-s^{4}(2s^2+1)(2s^2-1)\)
12. \(-p^{4}+64p^{2}=-p^{2}(p^2-64)=-p^{2}(p+8)(p-8)\)