Ontbinden in factoren (2)

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

1. \(180q^{6}-300q^{5}+125q^{4}\)
2. \(-16b^{15}-8b^{10}-b^{5}\)
3. \(16p^{13}+8p^{8}y+p^{3}y^2\)
4. \(-108a^{10}-180a^{6}-75a^{2}\)
5. \(y^{5}-64y^{3}\)
6. \(-2x^{7}+98x^{5}\)
7. \(-3x^{6}+192x^{4}\)
8. \(-6a^{5}+24a^{4}-24a^{3}\)
9. \(108b^{6}+36b^{4}x+3b^{2}x^2\)
10. \(-p^{4}+4p^{3}-4p^{2}\)
11. \(-98q^{4}+84q^{3}-18q^{2}\)
12. \(-48s^{11}+168s^{8}y-147s^{5}y^2\)

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

Verbetersleutel

1. \(180q^{6}-300q^{5}+125q^{4}=5q^{4}(36q^{2}-60q+25)=5q^{4}(6q-5)^2\)
2. \(-16b^{15}-8b^{10}-b^{5}=-b^{5}(16b^{10}+8b^5+1)=-b^{5}(4b^5+1)^2\)
3. \(16p^{13}+8p^{8}y+p^{3}y^2=p^{3}(16p^{10}+8p^5y+y^2)=p^{3}(4p^5+y)^2\)
4. \(-108a^{10}-180a^{6}-75a^{2}=-3a^{2}(36a^{8}+60a^4+25)=-3a^{2}(6a^4+5)^2\)
5. \(y^{5}-64y^{3}=y^{3}(y^2-64)=y^{3}(y+8)(y-8)\)
6. \(-2x^{7}+98x^{5}=-2x^{5}(x^2-49)=-2x^{5}(x+7)(x-7)\)
7. \(-3x^{6}+192x^{4}=-3x^{4}(x^2-64)=-3x^{4}(x+8)(x-8)\)
8. \(-6a^{5}+24a^{4}-24a^{3}=-6a^{3}(a^2-4a+4)=-6a^{3}(a-2)^2\)
9. \(108b^{6}+36b^{4}x+3b^{2}x^2=3b^{2}(36b^{4}+12b^2x+x^2)=3b^{2}(6b^2+x)^2\)
10. \(-p^{4}+4p^{3}-4p^{2}=-p^{2}(p^2-4p+4)=-p^{2}(p-2)^2\)
11. \(-98q^{4}+84q^{3}-18q^{2}=-2q^{2}(49q^{2}-42q+9)=-2q^{2}(7q-3)^2\)
12. \(-48s^{11}+168s^{8}y-147s^{5}y^2=-3s^{5}(16s^{6}-56s^3y+49y^2)=-3s^{5}(4s^3-7y)^2\)