Ontbinden in factoren (2)

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

1. \(108a^{9}-75a^{3}\)
2. \(32x^{6}+112x^{5}+98x^{4}\)
3. \(-294s^{9}+504s^{7}x-216s^{5}x^2\)
4. \(27a^{6}-147a^{4}\)
5. \(150p^{7}-240p^{5}+96p^{3}\)
6. \(-72s^{15}-24s^{10}-2s^{5}\)
7. \(-y^{6}+25y^{4}\)
8. \(80s^{5}-245s^{3}\)
9. \(245p^{11}+70p^{7}y+5p^{3}y^2\)
10. \(75a^{10}-12a^{4}\)
11. \(32y^{6}-50y^{4}\)
12. \(-12a^{8}+3a^{4}\)

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

Verbetersleutel

1. \(108a^{9}-75a^{3}=3a^{3}(36a^{6}-25)=3a^{3}(6a^3+5)(6a^3-5)\)
2. \(32x^{6}+112x^{5}+98x^{4}=2x^{4}(16x^{2}+56x+49)=2x^{4}(4x+7)^2\)
3. \(-294s^{9}+504s^{7}x-216s^{5}x^2=-6s^{5}(49s^{4}-84s^2x+36x^2)=-6s^{5}(7s^2-6x)^2\)
4. \(27a^{6}-147a^{4}=3a^{4}(9a^{2}-49)=3a^{4}(3a+7)(3a-7)\)
5. \(150p^{7}-240p^{5}+96p^{3}=6p^{3}(25p^{4}-40p^2+16)=6p^{3}(5p^2-4)^2\)
6. \(-72s^{15}-24s^{10}-2s^{5}=-2s^{5}(36s^{10}+12s^5+1)=-2s^{5}(6s^5+1)^2\)
7. \(-y^{6}+25y^{4}=-y^{4}(y^2-25)=-y^{4}(y+5)(y-5)\)
8. \(80s^{5}-245s^{3}=5s^{3}(16s^{2}-49)=5s^{3}(4s+7)(4s-7)\)
9. \(245p^{11}+70p^{7}y+5p^{3}y^2=5p^{3}(49p^{8}+14p^4y+y^2)=5p^{3}(7p^4+y)^2\)
10. \(75a^{10}-12a^{4}=3a^{4}(25a^{6}-4)=3a^{4}(5a^3+2)(5a^3-2)\)
11. \(32y^{6}-50y^{4}=2y^{4}(16y^{2}-25)=2y^{4}(4y+5)(4y-5)\)
12. \(-12a^{8}+3a^{4}=-3a^{4}(4a^{4}-1)=-3a^{4}(2a^2+1)(2a^2-1)\)