Ontbinden in factoren (2)

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

1. \(50s^{13}+80s^{9}+32s^{5}\)
2. \(5q^{4}+70q^{3}+245q^{2}\)
3. \(-80y^{9}-120y^{7}-45y^{5}\)
4. \(2q^{4}-128q^{2}\)
5. \(-80x^{7}+45x^{3}\)
6. \(2y^{7}-8y^{6}+8y^{5}\)
7. \(-54y^{11}-180y^{8}-150y^{5}\)
8. \(-36s^{12}-60s^{7}y-25s^{2}y^2\)
9. \(216p^{14}-150p^{4}\)
10. \(-2q^{6}+98q^{4}\)
11. \(-27b^{11}+90b^{7}-75b^{3}\)
12. \(72b^{5}-120b^{4}+50b^{3}\)

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

Verbetersleutel

1. \(50s^{13}+80s^{9}+32s^{5}=2s^{5}(25s^{8}+40s^4+16)=2s^{5}(5s^4+4)^2\)
2. \(5q^{4}+70q^{3}+245q^{2}=5q^{2}(q^2+14q+49)=5q^{2}(q+7)^2\)
3. \(-80y^{9}-120y^{7}-45y^{5}=-5y^{5}(16y^{4}+24y^2+9)=-5y^{5}(4y^2+3)^2\)
4. \(2q^{4}-128q^{2}=2q^{2}(q^2-64)=2q^{2}(q+8)(q-8)\)
5. \(-80x^{7}+45x^{3}=-5x^{3}(16x^{4}-9)=-5x^{3}(4x^2+3)(4x^2-3)\)
6. \(2y^{7}-8y^{6}+8y^{5}=2y^{5}(y^2-4y+4)=2y^{5}(y-2)^2\)
7. \(-54y^{11}-180y^{8}-150y^{5}=-6y^{5}(9y^{6}+30y^3+25)=-6y^{5}(3y^3+5)^2\)
8. \(-36s^{12}-60s^{7}y-25s^{2}y^2=-s^{2}(36s^{10}+60s^5y+25y^2)=-s^{2}(6s^5+5y)^2\)
9. \(216p^{14}-150p^{4}=6p^{4}(36p^{10}-25)=6p^{4}(6p^5+5)(6p^5-5)\)
10. \(-2q^{6}+98q^{4}=-2q^{4}(q^2-49)=-2q^{4}(q+7)(q-7)\)
11. \(-27b^{11}+90b^{7}-75b^{3}=-3b^{3}(9b^{8}-30b^4+25)=-3b^{3}(3b^4-5)^2\)
12. \(72b^{5}-120b^{4}+50b^{3}=2b^{3}(36b^{2}-60b+25)=2b^{3}(6b-5)^2\)