Ontbinden in factoren (2)

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

1. \(-4a^{5}+a^{3}\)
2. \(-36p^{12}-60p^{7}y-25p^{2}y^2\)
3. \(6b^{6}+24b^{5}+24b^{4}\)
4. \(3x^{6}-6x^{5}+3x^{4}\)
5. \(-27p^{18}+192p^{2}\)
6. \(-24p^{4}-216p^{3}-486p^{2}\)
7. \(-3a^{4}-6a^{3}-3a^{2}\)
8. \(-45b^{12}+60b^{8}s-20b^{4}s^2\)
9. \(-s^{5}+s^{3}\)
10. \(-125s^{9}-350s^{6}y-245s^{3}y^2\)
11. \(18q^{10}-128q^{4}\)
12. \(-80s^{14}-120s^{9}x-45s^{4}x^2\)

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

Verbetersleutel

1. \(-4a^{5}+a^{3}=-a^{3}(4a^{2}-1)=-a^{3}(2a+1)(2a-1)\)
2. \(-36p^{12}-60p^{7}y-25p^{2}y^2=-p^{2}(36p^{10}+60p^5y+25y^2)=-p^{2}(6p^5+5y)^2\)
3. \(6b^{6}+24b^{5}+24b^{4}=6b^{4}(b^2+4b+4)=6b^{4}(b+2)^2\)
4. \(3x^{6}-6x^{5}+3x^{4}=3x^{4}(x^2-2x+1)=3x^{4}(x-1)^2\)
5. \(-27p^{18}+192p^{2}=-3p^{2}(9p^{16}-64)=-3p^{2}(3p^8+8)(3p^8-8)\)
6. \(-24p^{4}-216p^{3}-486p^{2}=-6p^{2}(4p^{2}+36p+81)=-6p^{2}(2p+9)^2\)
7. \(-3a^{4}-6a^{3}-3a^{2}=-3a^{2}(a^2+2a+1)=-3a^{2}(a+1)^2\)
8. \(-45b^{12}+60b^{8}s-20b^{4}s^2=-5b^{4}(9b^{8}-12b^4s+4s^2)=-5b^{4}(3b^4-2s)^2\)
9. \(-s^{5}+s^{3}=-s^{3}(s^2-1)=-s^{3}(s+1)(s-1)\)
10. \(-125s^{9}-350s^{6}y-245s^{3}y^2=-5s^{3}(25s^{6}+70s^3y+49y^2)=-5s^{3}(5s^3+7y)^2\)
11. \(18q^{10}-128q^{4}=2q^{4}(9q^{6}-64)=2q^{4}(3q^3+8)(3q^3-8)\)
12. \(-80s^{14}-120s^{9}x-45s^{4}x^2=-5s^{4}(16s^{10}+24s^5x+9x^2)=-5s^{4}(4s^5+3x)^2\)