Ontbinden in factoren (2)

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

1. \(24q^{4}-294q^{2}\)
2. \(-x^{7}+x^{5}\)
3. \(-384p^{10}-96p^{7}s-6p^{4}s^2\)
4. \(50q^{7}-32q^{5}\)
5. \(-125b^{4}-200b^{3}-80b^{2}\)
6. \(-80a^{5}+125a^{3}\)
7. \(-45a^{16}+5a^{4}\)
8. \(-b^{4}+9b^{2}\)
9. \(36x^{13}-60x^{9}+25x^{5}\)
10. \(-108a^{8}-36a^{5}q-3a^{2}q^2\)
11. \(-3s^{5}+147s^{3}\)
12. \(80q^{9}-5q^{3}\)

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

Verbetersleutel

1. \(24q^{4}-294q^{2}=6q^{2}(4q^{2}-49)=6q^{2}(2q+7)(2q-7)\)
2. \(-x^{7}+x^{5}=-x^{5}(x^2-1)=-x^{5}(x-1)(x+1)\)
3. \(-384p^{10}-96p^{7}s-6p^{4}s^2=-6p^{4}(64p^{6}+16p^3s+s^2)=-6p^{4}(8p^3+s)^2\)
4. \(50q^{7}-32q^{5}=2q^{5}(25q^{2}-16)=2q^{5}(5q+4)(5q-4)\)
5. \(-125b^{4}-200b^{3}-80b^{2}=-5b^{2}(25b^{2}+40b+16)=-5b^{2}(5b+4)^2\)
6. \(-80a^{5}+125a^{3}=-5a^{3}(16a^{2}-25)=-5a^{3}(4a+5)(4a-5)\)
7. \(-45a^{16}+5a^{4}=-5a^{4}(9a^{12}-1)=-5a^{4}(3a^6+1)(3a^6-1)\)
8. \(-b^{4}+9b^{2}=-b^{2}(b^2-9)=-b^{2}(b+3)(b-3)\)
9. \(36x^{13}-60x^{9}+25x^{5}=x^{5}(36x^{8}-60x^4+25)=x^{5}(6x^4-5)^2\)
10. \(-108a^{8}-36a^{5}q-3a^{2}q^2=-3a^{2}(36a^{6}+12a^3q+q^2)=-3a^{2}(6a^3+q)^2\)
11. \(-3s^{5}+147s^{3}=-3s^{3}(s^2-49)=-3s^{3}(s+7)(s-7)\)
12. \(80q^{9}-5q^{3}=5q^{3}(16q^{6}-1)=5q^{3}(4q^3+1)(4q^3-1)\)