Ontbinden in factoren (2)

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

1. \(-32y^{7}+50y^{5}\)
2. \(50q^{4}-2q^{2}\)
3. \(125a^{11}+300a^{8}+180a^{5}\)
4. \(147x^{6}+42x^{5}+3x^{4}\)
5. \(-12x^{6}+3x^{4}\)
6. \(25y^{4}+10y^{3}+y^{2}\)
7. \(5q^{5}-90q^{4}+405q^{3}\)
8. \(72x^{5}-2x^{3}\)
9. \(-3a^{6}-30a^{5}-75a^{4}\)
10. \(-128s^{8}-32s^{5}x-2s^{2}x^2\)
11. \(-3s^{6}-42s^{5}-147s^{4}\)
12. \(75a^{9}-60a^{7}q+12a^{5}q^2\)

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

Verbetersleutel

1. \(-32y^{7}+50y^{5}=-2y^{5}(16y^{2}-25)=-2y^{5}(4y+5)(4y-5)\)
2. \(50q^{4}-2q^{2}=2q^{2}(25q^{2}-1)=2q^{2}(5q+1)(5q-1)\)
3. \(125a^{11}+300a^{8}+180a^{5}=5a^{5}(25a^{6}+60a^3+36)=5a^{5}(5a^3+6)^2\)
4. \(147x^{6}+42x^{5}+3x^{4}=3x^{4}(49x^{2}+14x+1)=3x^{4}(7x+1)^2\)
5. \(-12x^{6}+3x^{4}=-3x^{4}(4x^{2}-1)=-3x^{4}(2x+1)(2x-1)\)
6. \(25y^{4}+10y^{3}+y^{2}=y^{2}(25y^{2}+10y+1)=y^{2}(5y+1)^2\)
7. \(5q^{5}-90q^{4}+405q^{3}=5q^{3}(q^2-18q+81)=5q^{3}(q-9)^2\)
8. \(72x^{5}-2x^{3}=2x^{3}(36x^{2}-1)=2x^{3}(6x+1)(6x-1)\)
9. \(-3a^{6}-30a^{5}-75a^{4}=-3a^{4}(a^2+10a+25)=-3a^{4}(a+5)^2\)
10. \(-128s^{8}-32s^{5}x-2s^{2}x^2=-2s^{2}(64s^{6}+16s^3x+x^2)=-2s^{2}(8s^3+x)^2\)
11. \(-3s^{6}-42s^{5}-147s^{4}=-3s^{4}(s^2+14s+49)=-3s^{4}(s+7)^2\)
12. \(75a^{9}-60a^{7}q+12a^{5}q^2=3a^{5}(25a^{4}-20a^2q+4q^2)=3a^{5}(5a^2-2q)^2\)