Ontbinden in factoren (2)

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

1. \(-5a^{5}+50a^{4}-125a^{3}\)
2. \(-3b^{5}-36b^{4}-108b^{3}\)
3. \(-192b^{6}+240b^{5}-75b^{4}\)
4. \(-16y^{4}+9y^{2}\)
5. \(384b^{4}+96b^{3}+6b^{2}\)
6. \(-8q^{19}+98q^{5}\)
7. \(125q^{4}-80q^{2}\)
8. \(-24s^{8}-120s^{5}y-150s^{2}y^2\)
9. \(-54a^{11}+180a^{8}-150a^{5}\)
10. \(150a^{13}-216a^{5}\)
11. \(128y^{8}-224y^{6}+98y^{4}\)
12. \(-4s^{13}+s^{3}\)

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

Verbetersleutel

1. \(-5a^{5}+50a^{4}-125a^{3}=-5a^{3}(a^2-10a+25)=-5a^{3}(a-5)^2\)
2. \(-3b^{5}-36b^{4}-108b^{3}=-3b^{3}(b^2+12b+36)=-3b^{3}(b+6)^2\)
3. \(-192b^{6}+240b^{5}-75b^{4}=-3b^{4}(64b^{2}-80b+25)=-3b^{4}(8b-5)^2\)
4. \(-16y^{4}+9y^{2}=-y^{2}(16y^{2}-9)=-y^{2}(4y+3)(4y-3)\)
5. \(384b^{4}+96b^{3}+6b^{2}=6b^{2}(64b^{2}+16b+1)=6b^{2}(8b+1)^2\)
6. \(-8q^{19}+98q^{5}=-2q^{5}(4q^{14}-49)=-2q^{5}(2q^7+7)(2q^7-7)\)
7. \(125q^{4}-80q^{2}=5q^{2}(25q^{2}-16)=5q^{2}(5q+4)(5q-4)\)
8. \(-24s^{8}-120s^{5}y-150s^{2}y^2=-6s^{2}(4s^{6}+20s^3y+25y^2)=-6s^{2}(2s^3+5y)^2\)
9. \(-54a^{11}+180a^{8}-150a^{5}=-6a^{5}(9a^{6}-30a^3+25)=-6a^{5}(3a^3-5)^2\)
10. \(150a^{13}-216a^{5}=6a^{5}(25a^{8}-36)=6a^{5}(5a^4+6)(5a^4-6)\)
11. \(128y^{8}-224y^{6}+98y^{4}=2y^{4}(64y^{4}-112y^2+49)=2y^{4}(8y^2-7)^2\)
12. \(-4s^{13}+s^{3}=-s^{3}(4s^{10}-1)=-s^{3}(2s^5+1)(2s^5-1)\)