Ontbinden in factoren (2)

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

1. \(-80y^{14}+45y^{2}\)
2. \(p^{5}+2p^{4}+p^{3}\)
3. \(-36b^{4}+49b^{2}\)
4. \(45p^{7}-125p^{5}\)
5. \(216x^{10}-6x^{2}\)
6. \(2x^{5}-36x^{4}+162x^{3}\)
7. \(16s^{9}-9s^{5}\)
8. \(-125a^{9}-50a^{6}y-5a^{3}y^2\)
9. \(320a^{15}-400a^{10}b+125a^{5}b^2\)
10. \(-45p^{10}+150p^{7}-125p^{4}\)
11. \(192b^{15}+48b^{10}+3b^{5}\)
12. \(-192x^{7}-240x^{6}-75x^{5}\)

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

Verbetersleutel

1. \(-80y^{14}+45y^{2}=-5y^{2}(16y^{12}-9)=-5y^{2}(4y^6+3)(4y^6-3)\)
2. \(p^{5}+2p^{4}+p^{3}=p^{3}(p^2+2p+1)=p^{3}(p+1)^2\)
3. \(-36b^{4}+49b^{2}=-b^{2}(36b^{2}-49)=-b^{2}(6b+7)(6b-7)\)
4. \(45p^{7}-125p^{5}=5p^{5}(9p^{2}-25)=5p^{5}(3p+5)(3p-5)\)
5. \(216x^{10}-6x^{2}=6x^{2}(36x^{8}-1)=6x^{2}(6x^4+1)(6x^4-1)\)
6. \(2x^{5}-36x^{4}+162x^{3}=2x^{3}(x^2-18x+81)=2x^{3}(x-9)^2\)
7. \(16s^{9}-9s^{5}=s^{5}(16s^{4}-9)=s^{5}(4s^2+3)(4s^2-3)\)
8. \(-125a^{9}-50a^{6}y-5a^{3}y^2=-5a^{3}(25a^{6}+10a^3y+y^2)=-5a^{3}(5a^3+y)^2\)
9. \(320a^{15}-400a^{10}b+125a^{5}b^2=5a^{5}(64a^{10}-80a^5b+25b^2)=5a^{5}(8a^5-5b)^2\)
10. \(-45p^{10}+150p^{7}-125p^{4}=-5p^{4}(9p^{6}-30p^3+25)=-5p^{4}(3p^3-5)^2\)
11. \(192b^{15}+48b^{10}+3b^{5}=3b^{5}(64b^{10}+16b^5+1)=3b^{5}(8b^5+1)^2\)
12. \(-192x^{7}-240x^{6}-75x^{5}=-3x^{5}(64x^{2}+80x+25)=-3x^{5}(8x+5)^2\)