Ontbinden in factoren (2)

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

1. \(-12a^{5}-12a^{4}-3a^{3}\)
2. \(-80b^{7}-200b^{6}-125b^{5}\)
3. \(216x^{10}+360x^{6}+150x^{2}\)
4. \(-216q^{6}-360q^{4}y-150q^{2}y^2\)
5. \(4y^{11}-49y^{5}\)
6. \(12x^{6}-3x^{4}\)
7. \(-2a^{4}+72a^{2}\)
8. \(-50p^{5}+72p^{3}\)
9. \(-150b^{16}+96b^{2}\)
10. \(64y^{4}-112y^{3}+49y^{2}\)
11. \(-216p^{6}+360p^{4}-150p^{2}\)
12. \(80b^{17}-45b^{3}\)

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

Verbetersleutel

1. \(-12a^{5}-12a^{4}-3a^{3}=-3a^{3}(4a^{2}+4a+1)=-3a^{3}(2a+1)^2\)
2. \(-80b^{7}-200b^{6}-125b^{5}=-5b^{5}(16b^{2}+40b+25)=-5b^{5}(4b+5)^2\)
3. \(216x^{10}+360x^{6}+150x^{2}=6x^{2}(36x^{8}+60x^4+25)=6x^{2}(6x^4+5)^2\)
4. \(-216q^{6}-360q^{4}y-150q^{2}y^2=-6q^{2}(36q^{4}+60q^2y+25y^2)=-6q^{2}(6q^2+5y)^2\)
5. \(4y^{11}-49y^{5}=y^{5}(4y^{6}-49)=y^{5}(2y^3+7)(2y^3-7)\)
6. \(12x^{6}-3x^{4}=3x^{4}(4x^{2}-1)=3x^{4}(2x+1)(2x-1)\)
7. \(-2a^{4}+72a^{2}=-2a^{2}(a^2-36)=-2a^{2}(a+6)(a-6)\)
8. \(-50p^{5}+72p^{3}=-2p^{3}(25p^{2}-36)=-2p^{3}(5p+6)(5p-6)\)
9. \(-150b^{16}+96b^{2}=-6b^{2}(25b^{14}-16)=-6b^{2}(5b^7+4)(5b^7-4)\)
10. \(64y^{4}-112y^{3}+49y^{2}=y^{2}(64y^{2}-112y+49)=y^{2}(8y-7)^2\)
11. \(-216p^{6}+360p^{4}-150p^{2}=-6p^{2}(36p^{4}-60p^2+25)=-6p^{2}(6p^2-5)^2\)
12. \(80b^{17}-45b^{3}=5b^{3}(16b^{14}-9)=5b^{3}(4b^7+3)(4b^7-3)\)