Ontbinden in factoren (2)

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

1. \(-294b^{12}+504b^{8}-216b^{4}\)
2. \(-27b^{7}+48b^{5}\)
3. \(-50y^{14}+2y^{4}\)
4. \(-50x^{6}+140x^{5}-98x^{4}\)
5. \(-80b^{9}-200b^{6}-125b^{3}\)
6. \(125p^{8}-200p^{5}y+80p^{2}y^2\)
7. \(72x^{16}-50x^{4}\)
8. \(12b^{6}-27b^{4}\)
9. \(-12s^{5}-12s^{4}-3s^{3}\)
10. \(80y^{20}-5y^{4}\)
11. \(-q^{6}+8q^{5}-16q^{4}\)
12. \(98s^{7}+28s^{6}+2s^{5}\)

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

Verbetersleutel

1. \(-294b^{12}+504b^{8}-216b^{4}=-6b^{4}(49b^{8}-84b^4+36)=-6b^{4}(7b^4-6)^2\)
2. \(-27b^{7}+48b^{5}=-3b^{5}(9b^{2}-16)=-3b^{5}(3b+4)(3b-4)\)
3. \(-50y^{14}+2y^{4}=-2y^{4}(25y^{10}-1)=-2y^{4}(5y^5+1)(5y^5-1)\)
4. \(-50x^{6}+140x^{5}-98x^{4}=-2x^{4}(25x^{2}-70x+49)=-2x^{4}(5x-7)^2\)
5. \(-80b^{9}-200b^{6}-125b^{3}=-5b^{3}(16b^{6}+40b^3+25)=-5b^{3}(4b^3+5)^2\)
6. \(125p^{8}-200p^{5}y+80p^{2}y^2=5p^{2}(25p^{6}-40p^3y+16y^2)=5p^{2}(5p^3-4y)^2\)
7. \(72x^{16}-50x^{4}=2x^{4}(36x^{12}-25)=2x^{4}(6x^6+5)(6x^6-5)\)
8. \(12b^{6}-27b^{4}=3b^{4}(4b^{2}-9)=3b^{4}(2b+3)(2b-3)\)
9. \(-12s^{5}-12s^{4}-3s^{3}=-3s^{3}(4s^{2}+4s+1)=-3s^{3}(2s+1)^2\)
10. \(80y^{20}-5y^{4}=5y^{4}(16y^{16}-1)=5y^{4}(4y^8+1)(4y^8-1)\)
11. \(-q^{6}+8q^{5}-16q^{4}=-q^{4}(q^2-8q+16)=-q^{4}(q-4)^2\)
12. \(98s^{7}+28s^{6}+2s^{5}=2s^{5}(49s^{2}+14s+1)=2s^{5}(7s+1)^2\)