Ontbinden in factoren (2)

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

1. \(-25s^{14}+9s^{2}\)
2. \(-96s^{6}+294s^{4}\)
3. \(-8a^{5}+18a^{3}\)
4. \(294a^{6}-504a^{4}y+216a^{2}y^2\)
5. \(6p^{7}+60p^{6}+150p^{5}\)
6. \(-108y^{19}+147y^{3}\)
7. \(-108q^{21}+3q^{5}\)
8. \(54p^{4}-294p^{2}\)
9. \(48q^{9}-72q^{7}+27q^{5}\)
10. \(64a^{13}+112a^{8}p+49a^{3}p^2\)
11. \(27x^{6}-3x^{4}\)
12. \(6p^{6}+36p^{5}+54p^{4}\)

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

Verbetersleutel

1. \(-25s^{14}+9s^{2}=-s^{2}(25s^{12}-9)=-s^{2}(5s^6+3)(5s^6-3)\)
2. \(-96s^{6}+294s^{4}=-6s^{4}(16s^{2}-49)=-6s^{4}(4s+7)(4s-7)\)
3. \(-8a^{5}+18a^{3}=-2a^{3}(4a^{2}-9)=-2a^{3}(2a+3)(2a-3)\)
4. \(294a^{6}-504a^{4}y+216a^{2}y^2=6a^{2}(49a^{4}-84a^2y+36y^2)=6a^{2}(7a^2-6y)^2\)
5. \(6p^{7}+60p^{6}+150p^{5}=6p^{5}(p^2+10p+25)=6p^{5}(p+5)^2\)
6. \(-108y^{19}+147y^{3}=-3y^{3}(36y^{16}-49)=-3y^{3}(6y^8+7)(6y^8-7)\)
7. \(-108q^{21}+3q^{5}=-3q^{5}(36q^{16}-1)=-3q^{5}(6q^8+1)(6q^8-1)\)
8. \(54p^{4}-294p^{2}=6p^{2}(9p^{2}-49)=6p^{2}(3p+7)(3p-7)\)
9. \(48q^{9}-72q^{7}+27q^{5}=3q^{5}(16q^{4}-24q^2+9)=3q^{5}(4q^2-3)^2\)
10. \(64a^{13}+112a^{8}p+49a^{3}p^2=a^{3}(64a^{10}+112a^5p+49p^2)=a^{3}(8a^5+7p)^2\)
11. \(27x^{6}-3x^{4}=3x^{4}(9x^{2}-1)=3x^{4}(3x+1)(3x-1)\)
12. \(6p^{6}+36p^{5}+54p^{4}=6p^{4}(p^2+6p+9)=6p^{4}(p+3)^2\)