Ontbinden in factoren (2)

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

1. \(6a^{6}+72a^{5}+216a^{4}\)
2. \(2p^{6}+28p^{5}+98p^{4}\)
3. \(-5q^{4}+90q^{3}-405q^{2}\)
4. \(128p^{13}-160p^{9}x+50p^{5}x^2\)
5. \(-49s^{7}-70s^{5}y-25s^{3}y^2\)
6. \(-5y^{5}+60y^{4}-180y^{3}\)
7. \(-3b^{4}+18b^{3}-27b^{2}\)
8. \(75y^{21}-12y^{5}\)
9. \(-216x^{18}+6x^{2}\)
10. \(12p^{13}+12p^{9}q+3p^{5}q^2\)
11. \(-24p^{7}+150p^{5}\)
12. \(-192b^{13}+336b^{9}-147b^{5}\)

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

Verbetersleutel

1. \(6a^{6}+72a^{5}+216a^{4}=6a^{4}(a^2+12a+36)=6a^{4}(a+6)^2\)
2. \(2p^{6}+28p^{5}+98p^{4}=2p^{4}(p^2+14p+49)=2p^{4}(p+7)^2\)
3. \(-5q^{4}+90q^{3}-405q^{2}=-5q^{2}(q^2-18q+81)=-5q^{2}(q-9)^2\)
4. \(128p^{13}-160p^{9}x+50p^{5}x^2=2p^{5}(64p^{8}-80p^4x+25x^2)=2p^{5}(8p^4-5x)^2\)
5. \(-49s^{7}-70s^{5}y-25s^{3}y^2=-s^{3}(49s^{4}+70s^2y+25y^2)=-s^{3}(7s^2+5y)^2\)
6. \(-5y^{5}+60y^{4}-180y^{3}=-5y^{3}(y^2-12y+36)=-5y^{3}(y-6)^2\)
7. \(-3b^{4}+18b^{3}-27b^{2}=-3b^{2}(b^2-6b+9)=-3b^{2}(b-3)^2\)
8. \(75y^{21}-12y^{5}=3y^{5}(25y^{16}-4)=3y^{5}(5y^8+2)(5y^8-2)\)
9. \(-216x^{18}+6x^{2}=-6x^{2}(36x^{16}-1)=-6x^{2}(6x^8+1)(6x^8-1)\)
10. \(12p^{13}+12p^{9}q+3p^{5}q^2=3p^{5}(4p^{8}+4p^4q+q^2)=3p^{5}(2p^4+q)^2\)
11. \(-24p^{7}+150p^{5}=-6p^{5}(4p^{2}-25)=-6p^{5}(2p+5)(2p-5)\)
12. \(-192b^{13}+336b^{9}-147b^{5}=-3b^{5}(64b^{8}-112b^4+49)=-3b^{5}(8b^4-7)^2\)