Ontbinden in factoren (2)

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

1. \(-3y^{5}+12y^{4}-12y^{3}\)
2. \(-2b^{4}+98b^{2}\)
3. \(27y^{8}-12y^{2}\)
4. \(-p^{4}-18p^{3}-81p^{2}\)
5. \(-2b^{7}-8b^{6}-8b^{5}\)
6. \(-5y^{5}+180y^{3}\)
7. \(-48a^{14}+72a^{9}b-27a^{4}b^2\)
8. \(s^{4}-2s^{3}+s^{2}\)
9. \(2x^{6}+28x^{5}+98x^{4}\)
10. \(-54a^{6}+72a^{4}-24a^{2}\)
11. \(-20p^{12}-20p^{7}y-5p^{2}y^2\)
12. \(6b^{6}+36b^{5}+54b^{4}\)

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

Verbetersleutel

1. \(-3y^{5}+12y^{4}-12y^{3}=-3y^{3}(y^2-4y+4)=-3y^{3}(y-2)^2\)
2. \(-2b^{4}+98b^{2}=-2b^{2}(b^2-49)=-2b^{2}(b+7)(b-7)\)
3. \(27y^{8}-12y^{2}=3y^{2}(9y^{6}-4)=3y^{2}(3y^3+2)(3y^3-2)\)
4. \(-p^{4}-18p^{3}-81p^{2}=-p^{2}(p^2+18p+81)=-p^{2}(p+9)^2\)
5. \(-2b^{7}-8b^{6}-8b^{5}=-2b^{5}(b^2+4b+4)=-2b^{5}(b+2)^2\)
6. \(-5y^{5}+180y^{3}=-5y^{3}(y^2-36)=-5y^{3}(y+6)(y-6)\)
7. \(-48a^{14}+72a^{9}b-27a^{4}b^2=-3a^{4}(16a^{10}-24a^5b+9b^2)=-3a^{4}(4a^5-3b)^2\)
8. \(s^{4}-2s^{3}+s^{2}=s^{2}(s^2-2s+1)=s^{2}(s-1)^2\)
9. \(2x^{6}+28x^{5}+98x^{4}=2x^{4}(x^2+14x+49)=2x^{4}(x+7)^2\)
10. \(-54a^{6}+72a^{4}-24a^{2}=-6a^{2}(9a^{4}-12a^2+4)=-6a^{2}(3a^2-2)^2\)
11. \(-20p^{12}-20p^{7}y-5p^{2}y^2=-5p^{2}(4p^{10}+4p^5y+y^2)=-5p^{2}(2p^5+y)^2\)
12. \(6b^{6}+36b^{5}+54b^{4}=6b^{4}(b^2+6b+9)=6b^{4}(b+3)^2\)