Ontbinden in factoren (2)

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

1. \(192q^{5}-240q^{4}+75q^{3}\)
2. \(-p^{5}+p^{3}\)
3. \(3a^{7}-147a^{5}\)
4. \(18a^{7}-2a^{5}\)
5. \(4q^{11}-9q^{3}\)
6. \(9b^{18}-4b^{2}\)
7. \(6y^{6}-24y^{4}\)
8. \(-108x^{9}-36x^{7}-3x^{5}\)
9. \(75s^{19}-48s^{5}\)
10. \(-150x^{7}-60x^{6}-6x^{5}\)
11. \(108x^{15}-3x^{5}\)
12. \(-80a^{6}-120a^{4}y-45a^{2}y^2\)

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

Verbetersleutel

1. \(192q^{5}-240q^{4}+75q^{3}=3q^{3}(64q^{2}-80q+25)=3q^{3}(8q-5)^2\)
2. \(-p^{5}+p^{3}=-p^{3}(p^2-1)=-p^{3}(p+1)(p-1)\)
3. \(3a^{7}-147a^{5}=3a^{5}(a^2-49)=3a^{5}(a-7)(a+7)\)
4. \(18a^{7}-2a^{5}=2a^{5}(9a^{2}-1)=2a^{5}(3a+1)(3a-1)\)
5. \(4q^{11}-9q^{3}=q^{3}(4q^{8}-9)=q^{3}(2q^4+3)(2q^4-3)\)
6. \(9b^{18}-4b^{2}=b^{2}(9b^{16}-4)=b^{2}(3b^8+2)(3b^8-2)\)
7. \(6y^{6}-24y^{4}=6y^{4}(y^2-4)=6y^{4}(y+2)(y-2)\)
8. \(-108x^{9}-36x^{7}-3x^{5}=-3x^{5}(36x^{4}+12x^2+1)=-3x^{5}(6x^2+1)^2\)
9. \(75s^{19}-48s^{5}=3s^{5}(25s^{14}-16)=3s^{5}(5s^7+4)(5s^7-4)\)
10. \(-150x^{7}-60x^{6}-6x^{5}=-6x^{5}(25x^{2}+10x+1)=-6x^{5}(5x+1)^2\)
11. \(108x^{15}-3x^{5}=3x^{5}(36x^{10}-1)=3x^{5}(6x^5+1)(6x^5-1)\)
12. \(-80a^{6}-120a^{4}y-45a^{2}y^2=-5a^{2}(16a^{4}+24a^2y+9y^2)=-5a^{2}(4a^2+3y)^2\)