Ontbinden in factoren (2)

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

1. \(a^{7}-18a^{6}+81a^{5}\)
2. \(-6a^{7}+96a^{6}-384a^{5}\)
3. \(-24a^{4}-24a^{3}-6a^{2}\)
4. \(18y^{19}-2y^{5}\)
5. \(27p^{15}+18p^{10}+3p^{5}\)
6. \(a^{4}-25a^{2}\)
7. \(3q^{6}+6q^{5}+3q^{4}\)
8. \(-24p^{7}-120p^{5}x-150p^{3}x^2\)
9. \(384a^{7}-480a^{6}+150a^{5}\)
10. \(96p^{21}-294p^{5}\)
11. \(-18y^{12}+60y^{7}-50y^{2}\)
12. \(2s^{5}-18s^{3}\)

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

Verbetersleutel

1. \(a^{7}-18a^{6}+81a^{5}=a^{5}(a^2-18a+81)=a^{5}(a-9)^2\)
2. \(-6a^{7}+96a^{6}-384a^{5}=-6a^{5}(a^2-16a+64)=-6a^{5}(a-8)^2\)
3. \(-24a^{4}-24a^{3}-6a^{2}=-6a^{2}(4a^{2}+4a+1)=-6a^{2}(2a+1)^2\)
4. \(18y^{19}-2y^{5}=2y^{5}(9y^{14}-1)=2y^{5}(3y^7+1)(3y^7-1)\)
5. \(27p^{15}+18p^{10}+3p^{5}=3p^{5}(9p^{10}+6p^5+1)=3p^{5}(3p^5+1)^2\)
6. \(a^{4}-25a^{2}=a^{2}(a^2-25)=a^{2}(a+5)(a-5)\)
7. \(3q^{6}+6q^{5}+3q^{4}=3q^{4}(q^2+2q+1)=3q^{4}(q+1)^2\)
8. \(-24p^{7}-120p^{5}x-150p^{3}x^2=-6p^{3}(4p^{4}+20p^2x+25x^2)=-6p^{3}(2p^2+5x)^2\)
9. \(384a^{7}-480a^{6}+150a^{5}=6a^{5}(64a^{2}-80a+25)=6a^{5}(8a-5)^2\)
10. \(96p^{21}-294p^{5}=6p^{5}(16p^{16}-49)=6p^{5}(4p^8+7)(4p^8-7)\)
11. \(-18y^{12}+60y^{7}-50y^{2}=-2y^{2}(9y^{10}-30y^5+25)=-2y^{2}(3y^5-5)^2\)
12. \(2s^{5}-18s^{3}=2s^{3}(s^2-9)=2s^{3}(s-3)(s+3)\)