Ontbinden in factoren (2)

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

1. \(9s^{7}-4s^{3}\)
2. \(-24x^{12}-24x^{8}-6x^{4}\)
3. \(6b^{4}+60b^{3}+150b^{2}\)
4. \(16x^{11}+8x^{7}+x^{3}\)
5. \(a^{5}-64a^{3}\)
6. \(-16y^{7}+y^{5}\)
7. \(12q^{4}-3q^{2}\)
8. \(-96p^{8}-48p^{6}-6p^{4}\)
9. \(216a^{7}+72a^{6}+6a^{5}\)
10. \(-96p^{7}+54p^{5}\)
11. \(-54s^{6}+150s^{4}\)
12. \(-5x^{4}+20x^{2}\)

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

Verbetersleutel

1. \(9s^{7}-4s^{3}=s^{3}(9s^{4}-4)=s^{3}(3s^2+2)(3s^2-2)\)
2. \(-24x^{12}-24x^{8}-6x^{4}=-6x^{4}(4x^{8}+4x^4+1)=-6x^{4}(2x^4+1)^2\)
3. \(6b^{4}+60b^{3}+150b^{2}=6b^{2}(b^2+10b+25)=6b^{2}(b+5)^2\)
4. \(16x^{11}+8x^{7}+x^{3}=x^{3}(16x^{8}+8x^4+1)=x^{3}(4x^4+1)^2\)
5. \(a^{5}-64a^{3}=a^{3}(a^2-64)=a^{3}(a+8)(a-8)\)
6. \(-16y^{7}+y^{5}=-y^{5}(16y^{2}-1)=-y^{5}(4y+1)(4y-1)\)
7. \(12q^{4}-3q^{2}=3q^{2}(4q^{2}-1)=3q^{2}(2q+1)(2q-1)\)
8. \(-96p^{8}-48p^{6}-6p^{4}=-6p^{4}(16p^{4}+8p^2+1)=-6p^{4}(4p^2+1)^2\)
9. \(216a^{7}+72a^{6}+6a^{5}=6a^{5}(36a^{2}+12a+1)=6a^{5}(6a+1)^2\)
10. \(-96p^{7}+54p^{5}=-6p^{5}(16p^{2}-9)=-6p^{5}(4p+3)(4p-3)\)
11. \(-54s^{6}+150s^{4}=-6s^{4}(9s^{2}-25)=-6s^{4}(3s+5)(3s-5)\)
12. \(-5x^{4}+20x^{2}=-5x^{2}(x^2-4)=-5x^{2}(x+2)(x-2)\)