Ontbinden in factoren (2)

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

1. \(216y^{19}-150y^{3}\)
2. \(-36p^{12}+49p^{4}\)
3. \(5a^{6}-80a^{5}+320a^{4}\)
4. \(2b^{7}-18b^{5}\)
5. \(25s^{9}-20s^{7}+4s^{5}\)
6. \(-72y^{5}-168y^{4}-98y^{3}\)
7. \(-2y^{6}+128y^{4}\)
8. \(-24s^{4}+6s^{2}\)
9. \(-108p^{5}+3p^{3}\)
10. \(-54x^{4}-72x^{3}-24x^{2}\)
11. \(3p^{6}-3p^{4}\)
12. \(-54a^{6}+6a^{4}\)

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

Verbetersleutel

1. \(216y^{19}-150y^{3}=6y^{3}(36y^{16}-25)=6y^{3}(6y^8+5)(6y^8-5)\)
2. \(-36p^{12}+49p^{4}=-p^{4}(36p^{8}-49)=-p^{4}(6p^4+7)(6p^4-7)\)
3. \(5a^{6}-80a^{5}+320a^{4}=5a^{4}(a^2-16a+64)=5a^{4}(a-8)^2\)
4. \(2b^{7}-18b^{5}=2b^{5}(b^2-9)=2b^{5}(b-3)(b+3)\)
5. \(25s^{9}-20s^{7}+4s^{5}=s^{5}(25s^{4}-20s^2+4)=s^{5}(5s^2-2)^2\)
6. \(-72y^{5}-168y^{4}-98y^{3}=-2y^{3}(36y^{2}+84y+49)=-2y^{3}(6y+7)^2\)
7. \(-2y^{6}+128y^{4}=-2y^{4}(y^2-64)=-2y^{4}(y+8)(y-8)\)
8. \(-24s^{4}+6s^{2}=-6s^{2}(4s^{2}-1)=-6s^{2}(2s+1)(2s-1)\)
9. \(-108p^{5}+3p^{3}=-3p^{3}(36p^{2}-1)=-3p^{3}(6p+1)(6p-1)\)
10. \(-54x^{4}-72x^{3}-24x^{2}=-6x^{2}(9x^{2}+12x+4)=-6x^{2}(3x+2)^2\)
11. \(3p^{6}-3p^{4}=3p^{4}(p^2-1)=3p^{4}(p-1)(p+1)\)
12. \(-54a^{6}+6a^{4}=-6a^{4}(9a^{2}-1)=-6a^{4}(3a+1)(3a-1)\)