Ontbinden in factoren (2)

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

1. \(-p^{4}+64p^{2}\)
2. \(-80q^{13}+120q^{8}s-45q^{3}s^2\)
3. \(16s^{14}-49s^{2}\)
4. \(6x^{6}-24x^{4}\)
5. \(25s^{6}-16s^{4}\)
6. \(-49b^{12}-14b^{8}-b^{4}\)
7. \(-2s^{5}+36s^{4}-162s^{3}\)
8. \(6p^{7}-54p^{5}\)
9. \(-9b^{5}+12b^{4}-4b^{3}\)
10. \(-5q^{7}+180q^{5}\)
11. \(75a^{7}-48a^{5}\)
12. \(-16s^{7}+9s^{5}\)

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

Verbetersleutel

1. \(-p^{4}+64p^{2}=-p^{2}(p^2-64)=-p^{2}(p+8)(p-8)\)
2. \(-80q^{13}+120q^{8}s-45q^{3}s^2=-5q^{3}(16q^{10}-24q^5s+9s^2)=-5q^{3}(4q^5-3s)^2\)
3. \(16s^{14}-49s^{2}=s^{2}(16s^{12}-49)=s^{2}(4s^6+7)(4s^6-7)\)
4. \(6x^{6}-24x^{4}=6x^{4}(x^2-4)=6x^{4}(x+2)(x-2)\)
5. \(25s^{6}-16s^{4}=s^{4}(25s^{2}-16)=s^{4}(5s+4)(5s-4)\)
6. \(-49b^{12}-14b^{8}-b^{4}=-b^{4}(49b^{8}+14b^4+1)=-b^{4}(7b^4+1)^2\)
7. \(-2s^{5}+36s^{4}-162s^{3}=-2s^{3}(s^2-18s+81)=-2s^{3}(s-9)^2\)
8. \(6p^{7}-54p^{5}=6p^{5}(p^2-9)=6p^{5}(p-3)(p+3)\)
9. \(-9b^{5}+12b^{4}-4b^{3}=-b^{3}(9b^{2}-12b+4)=-b^{3}(3b-2)^2\)
10. \(-5q^{7}+180q^{5}=-5q^{5}(q^2-36)=-5q^{5}(q+6)(q-6)\)
11. \(75a^{7}-48a^{5}=3a^{5}(25a^{2}-16)=3a^{5}(5a+4)(5a-4)\)
12. \(-16s^{7}+9s^{5}=-s^{5}(16s^{2}-9)=-s^{5}(4s+3)(4s-3)\)