Ontbinden in factoren (2)

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

1. \(-80a^{5}+5a^{3}\)
2. \(-96p^{12}-240p^{8}q-150p^{4}q^2\)
3. \(16x^{5}-x^{3}\)
4. \(-6x^{7}+12x^{6}-6x^{5}\)
5. \(-12q^{6}-12q^{5}-3q^{4}\)
6. \(-18b^{5}+2b^{3}\)
7. \(24a^{13}-54a^{3}\)
8. \(-2a^{4}+8a^{2}\)
9. \(4s^{14}+4s^{9}+s^{4}\)
10. \(27q^{11}-36q^{7}+12q^{3}\)
11. \(150a^{9}-240a^{7}x+96a^{5}x^2\)
12. \(20a^{10}+20a^{7}y+5a^{4}y^2\)

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

Verbetersleutel

1. \(-80a^{5}+5a^{3}=-5a^{3}(16a^{2}-1)=-5a^{3}(4a+1)(4a-1)\)
2. \(-96p^{12}-240p^{8}q-150p^{4}q^2=-6p^{4}(16p^{8}+40p^4q+25q^2)=-6p^{4}(4p^4+5q)^2\)
3. \(16x^{5}-x^{3}=x^{3}(16x^{2}-1)=x^{3}(4x+1)(4x-1)\)
4. \(-6x^{7}+12x^{6}-6x^{5}=-6x^{5}(x^2-2x+1)=-6x^{5}(x-1)^2\)
5. \(-12q^{6}-12q^{5}-3q^{4}=-3q^{4}(4q^{2}+4q+1)=-3q^{4}(2q+1)^2\)
6. \(-18b^{5}+2b^{3}=-2b^{3}(9b^{2}-1)=-2b^{3}(3b+1)(3b-1)\)
7. \(24a^{13}-54a^{3}=6a^{3}(4a^{10}-9)=6a^{3}(2a^5+3)(2a^5-3)\)
8. \(-2a^{4}+8a^{2}=-2a^{2}(a^2-4)=-2a^{2}(a-2)(a+2)\)
9. \(4s^{14}+4s^{9}+s^{4}=s^{4}(4s^{10}+4s^5+1)=s^{4}(2s^5+1)^2\)
10. \(27q^{11}-36q^{7}+12q^{3}=3q^{3}(9q^{8}-12q^4+4)=3q^{3}(3q^4-2)^2\)
11. \(150a^{9}-240a^{7}x+96a^{5}x^2=6a^{5}(25a^{4}-40a^2x+16x^2)=6a^{5}(5a^2-4x)^2\)
12. \(20a^{10}+20a^{7}y+5a^{4}y^2=5a^{4}(4a^{6}+4a^3y+y^2)=5a^{4}(2a^3+y)^2\)