Ontbinden in factoren (2)

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

1. \(-50y^{14}+40y^{9}-8y^{4}\)
2. \(16a^{13}-49a^{5}\)
3. \(-32p^{14}+48p^{9}-18p^{4}\)
4. \(-4p^{5}+25p^{3}\)
5. \(12a^{6}+12a^{5}+3a^{4}\)
6. \(2s^{6}+12s^{5}+18s^{4}\)
7. \(-72x^{6}-24x^{4}-2x^{2}\)
8. \(18b^{19}-50b^{3}\)
9. \(-49q^{6}+84q^{5}-36q^{4}\)
10. \(-6y^{7}-84y^{6}-294y^{5}\)
11. \(-a^{6}+9a^{4}\)
12. \(98y^{11}+140y^{8}+50y^{5}\)

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

Verbetersleutel

1. \(-50y^{14}+40y^{9}-8y^{4}=-2y^{4}(25y^{10}-20y^5+4)=-2y^{4}(5y^5-2)^2\)
2. \(16a^{13}-49a^{5}=a^{5}(16a^{8}-49)=a^{5}(4a^4+7)(4a^4-7)\)
3. \(-32p^{14}+48p^{9}-18p^{4}=-2p^{4}(16p^{10}-24p^5+9)=-2p^{4}(4p^5-3)^2\)
4. \(-4p^{5}+25p^{3}=-p^{3}(4p^{2}-25)=-p^{3}(2p+5)(2p-5)\)
5. \(12a^{6}+12a^{5}+3a^{4}=3a^{4}(4a^{2}+4a+1)=3a^{4}(2a+1)^2\)
6. \(2s^{6}+12s^{5}+18s^{4}=2s^{4}(s^2+6s+9)=2s^{4}(s+3)^2\)
7. \(-72x^{6}-24x^{4}-2x^{2}=-2x^{2}(36x^{4}+12x^2+1)=-2x^{2}(6x^2+1)^2\)
8. \(18b^{19}-50b^{3}=2b^{3}(9b^{16}-25)=2b^{3}(3b^8+5)(3b^8-5)\)
9. \(-49q^{6}+84q^{5}-36q^{4}=-q^{4}(49q^{2}-84q+36)=-q^{4}(7q-6)^2\)
10. \(-6y^{7}-84y^{6}-294y^{5}=-6y^{5}(y^2+14y+49)=-6y^{5}(y+7)^2\)
11. \(-a^{6}+9a^{4}=-a^{4}(a^2-9)=-a^{4}(a+3)(a-3)\)
12. \(98y^{11}+140y^{8}+50y^{5}=2y^{5}(49y^{6}+70y^3+25)=2y^{5}(7y^3+5)^2\)