Ontbinden in factoren (2)

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

1. \(36x^{5}-x^{3}\)
2. \(50b^{5}-2b^{3}\)
3. \(-20b^{11}+5b^{3}\)
4. \(-8y^{4}-8y^{3}-2y^{2}\)
5. \(-98q^{6}-84q^{4}s-18q^{2}s^2\)
6. \(-8q^{10}-8q^{7}-2q^{4}\)
7. \(-180x^{10}-60x^{6}y-5x^{2}y^2\)
8. \(72a^{7}-50a^{5}\)
9. \(-6q^{7}+216q^{5}\)
10. \(-p^{5}+25p^{3}\)
11. \(-294b^{13}-504b^{9}-216b^{5}\)
12. \(12b^{4}-147b^{2}\)

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

Verbetersleutel

1. \(36x^{5}-x^{3}=x^{3}(36x^{2}-1)=x^{3}(6x+1)(6x-1)\)
2. \(50b^{5}-2b^{3}=2b^{3}(25b^{2}-1)=2b^{3}(5b+1)(5b-1)\)
3. \(-20b^{11}+5b^{3}=-5b^{3}(4b^{8}-1)=-5b^{3}(2b^4+1)(2b^4-1)\)
4. \(-8y^{4}-8y^{3}-2y^{2}=-2y^{2}(4y^{2}+4y+1)=-2y^{2}(2y+1)^2\)
5. \(-98q^{6}-84q^{4}s-18q^{2}s^2=-2q^{2}(49q^{4}+42q^2s+9s^2)=-2q^{2}(7q^2+3s)^2\)
6. \(-8q^{10}-8q^{7}-2q^{4}=-2q^{4}(4q^{6}+4q^3+1)=-2q^{4}(2q^3+1)^2\)
7. \(-180x^{10}-60x^{6}y-5x^{2}y^2=-5x^{2}(36x^{8}+12x^4y+y^2)=-5x^{2}(6x^4+y)^2\)
8. \(72a^{7}-50a^{5}=2a^{5}(36a^{2}-25)=2a^{5}(6a+5)(6a-5)\)
9. \(-6q^{7}+216q^{5}=-6q^{5}(q^2-36)=-6q^{5}(q+6)(q-6)\)
10. \(-p^{5}+25p^{3}=-p^{3}(p^2-25)=-p^{3}(p-5)(p+5)\)
11. \(-294b^{13}-504b^{9}-216b^{5}=-6b^{5}(49b^{8}+84b^4+36)=-6b^{5}(7b^4+6)^2\)
12. \(12b^{4}-147b^{2}=3b^{2}(4b^{2}-49)=3b^{2}(2b+7)(2b-7)\)