Ontbinden in factoren (2)

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

1. \(150y^{4}-54y^{2}\)
2. \(245a^{13}+70a^{9}x+5a^{5}x^2\)
3. \(-45y^{7}-60y^{6}-20y^{5}\)
4. \(-2x^{6}+50x^{4}\)
5. \(-16a^{5}-8a^{4}-a^{3}\)
6. \(-128q^{6}-160q^{5}-50q^{4}\)
7. \(-150a^{7}+6a^{5}\)
8. \(y^{5}-4y^{3}\)
9. \(6x^{7}-6x^{5}\)
10. \(-45a^{8}+125a^{4}\)
11. \(-96s^{10}+336s^{7}-294s^{4}\)
12. \(-54y^{6}-180y^{5}-150y^{4}\)

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

Verbetersleutel

1. \(150y^{4}-54y^{2}=6y^{2}(25y^{2}-9)=6y^{2}(5y+3)(5y-3)\)
2. \(245a^{13}+70a^{9}x+5a^{5}x^2=5a^{5}(49a^{8}+14a^4x+x^2)=5a^{5}(7a^4+x)^2\)
3. \(-45y^{7}-60y^{6}-20y^{5}=-5y^{5}(9y^{2}+12y+4)=-5y^{5}(3y+2)^2\)
4. \(-2x^{6}+50x^{4}=-2x^{4}(x^2-25)=-2x^{4}(x+5)(x-5)\)
5. \(-16a^{5}-8a^{4}-a^{3}=-a^{3}(16a^{2}+8a+1)=-a^{3}(4a+1)^2\)
6. \(-128q^{6}-160q^{5}-50q^{4}=-2q^{4}(64q^{2}+80q+25)=-2q^{4}(8q+5)^2\)
7. \(-150a^{7}+6a^{5}=-6a^{5}(25a^{2}-1)=-6a^{5}(5a+1)(5a-1)\)
8. \(y^{5}-4y^{3}=y^{3}(y^2-4)=y^{3}(y-2)(y+2)\)
9. \(6x^{7}-6x^{5}=6x^{5}(x^2-1)=6x^{5}(x-1)(x+1)\)
10. \(-45a^{8}+125a^{4}=-5a^{4}(9a^{4}-25)=-5a^{4}(3a^2+5)(3a^2-5)\)
11. \(-96s^{10}+336s^{7}-294s^{4}=-6s^{4}(16s^{6}-56s^3+49)=-6s^{4}(4s^3-7)^2\)
12. \(-54y^{6}-180y^{5}-150y^{4}=-6y^{4}(9y^{2}+30y+25)=-6y^{4}(3y+5)^2\)