Ontbinden in factoren (2)

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

1. \(-25x^{14}+36x^{4}\)
2. \(-9a^{9}+12a^{6}y-4a^{3}y^2\)
3. \(-150b^{12}-60b^{8}-6b^{4}\)
4. \(-49y^{15}-42y^{10}-9y^{5}\)
5. \(18q^{6}-32q^{4}\)
6. \(-45p^{7}-240p^{6}-320p^{5}\)
7. \(-32x^{5}+48x^{4}-18x^{3}\)
8. \(-3b^{5}+75b^{3}\)
9. \(-128p^{13}+160p^{9}-50p^{5}\)
10. \(-75s^{19}+108s^{5}\)
11. \(8b^{7}+8b^{5}+2b^{3}\)
12. \(-16p^{13}-8p^{8}y-p^{3}y^2\)

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

Verbetersleutel

1. \(-25x^{14}+36x^{4}=-x^{4}(25x^{10}-36)=-x^{4}(5x^5+6)(5x^5-6)\)
2. \(-9a^{9}+12a^{6}y-4a^{3}y^2=-a^{3}(9a^{6}-12a^3y+4y^2)=-a^{3}(3a^3-2y)^2\)
3. \(-150b^{12}-60b^{8}-6b^{4}=-6b^{4}(25b^{8}+10b^4+1)=-6b^{4}(5b^4+1)^2\)
4. \(-49y^{15}-42y^{10}-9y^{5}=-y^{5}(49y^{10}+42y^5+9)=-y^{5}(7y^5+3)^2\)
5. \(18q^{6}-32q^{4}=2q^{4}(9q^{2}-16)=2q^{4}(3q+4)(3q-4)\)
6. \(-45p^{7}-240p^{6}-320p^{5}=-5p^{5}(9p^{2}+48p+64)=-5p^{5}(3p+8)^2\)
7. \(-32x^{5}+48x^{4}-18x^{3}=-2x^{3}(16x^{2}-24x+9)=-2x^{3}(4x-3)^2\)
8. \(-3b^{5}+75b^{3}=-3b^{3}(b^2-25)=-3b^{3}(b+5)(b-5)\)
9. \(-128p^{13}+160p^{9}-50p^{5}=-2p^{5}(64p^{8}-80p^4+25)=-2p^{5}(8p^4-5)^2\)
10. \(-75s^{19}+108s^{5}=-3s^{5}(25s^{14}-36)=-3s^{5}(5s^7+6)(5s^7-6)\)
11. \(8b^{7}+8b^{5}+2b^{3}=2b^{3}(4b^{4}+4b^2+1)=2b^{3}(2b^2+1)^2\)
12. \(-16p^{13}-8p^{8}y-p^{3}y^2=-p^{3}(16p^{10}+8p^5y+y^2)=-p^{3}(4p^5+y)^2\)