Ontbinden in factoren (2)

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

1. \(49y^{5}+28y^{4}+4y^{3}\)
2. \(5p^{5}-80p^{3}\)
3. \(-216s^{7}+360s^{6}-150s^{5}\)
4. \(-48b^{6}+168b^{5}-147b^{4}\)
5. \(-108x^{8}+75x^{2}\)
6. \(-18x^{5}+2x^{3}\)
7. \(-245a^{13}-350a^{9}x-125a^{5}x^2\)
8. \(-54b^{8}+150b^{4}\)
9. \(3p^{7}+12p^{6}+12p^{5}\)
10. \(150s^{5}-216s^{3}\)
11. \(-32y^{14}+2y^{2}\)
12. \(-2s^{4}+16s^{3}-32s^{2}\)

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

Verbetersleutel

1. \(49y^{5}+28y^{4}+4y^{3}=y^{3}(49y^{2}+28y+4)=y^{3}(7y+2)^2\)
2. \(5p^{5}-80p^{3}=5p^{3}(p^2-16)=5p^{3}(p+4)(p-4)\)
3. \(-216s^{7}+360s^{6}-150s^{5}=-6s^{5}(36s^{2}-60s+25)=-6s^{5}(6s-5)^2\)
4. \(-48b^{6}+168b^{5}-147b^{4}=-3b^{4}(16b^{2}-56b+49)=-3b^{4}(4b-7)^2\)
5. \(-108x^{8}+75x^{2}=-3x^{2}(36x^{6}-25)=-3x^{2}(6x^3+5)(6x^3-5)\)
6. \(-18x^{5}+2x^{3}=-2x^{3}(9x^{2}-1)=-2x^{3}(3x+1)(3x-1)\)
7. \(-245a^{13}-350a^{9}x-125a^{5}x^2=-5a^{5}(49a^{8}+70a^4x+25x^2)=-5a^{5}(7a^4+5x)^2\)
8. \(-54b^{8}+150b^{4}=-6b^{4}(9b^{4}-25)=-6b^{4}(3b^2+5)(3b^2-5)\)
9. \(3p^{7}+12p^{6}+12p^{5}=3p^{5}(p^2+4p+4)=3p^{5}(p+2)^2\)
10. \(150s^{5}-216s^{3}=6s^{3}(25s^{2}-36)=6s^{3}(5s+6)(5s-6)\)
11. \(-32y^{14}+2y^{2}=-2y^{2}(16y^{12}-1)=-2y^{2}(4y^6+1)(4y^6-1)\)
12. \(-2s^{4}+16s^{3}-32s^{2}=-2s^{2}(s^2-8s+16)=-2s^{2}(s-4)^2\)