Ontbinden in factoren (2)

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

1. \(18x^{5}-98x^{3}\)
2. \(-27b^{13}+36b^{8}-12b^{3}\)
3. \(-192b^{8}-48b^{6}p-3b^{4}p^2\)
4. \(-16s^{21}+25s^{5}\)
5. \(9b^{8}-49b^{2}\)
6. \(-9y^{7}+y^{5}\)
7. \(5y^{6}-50y^{5}+125y^{4}\)
8. \(-75b^{4}-90b^{3}-27b^{2}\)
9. \(y^{7}-10y^{6}+25y^{5}\)
10. \(25a^{14}-70a^{9}y+49a^{4}y^2\)
11. \(108p^{7}-147p^{5}\)
12. \(-216b^{11}+360b^{8}y-150b^{5}y^2\)

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

Verbetersleutel

1. \(18x^{5}-98x^{3}=2x^{3}(9x^{2}-49)=2x^{3}(3x+7)(3x-7)\)
2. \(-27b^{13}+36b^{8}-12b^{3}=-3b^{3}(9b^{10}-12b^5+4)=-3b^{3}(3b^5-2)^2\)
3. \(-192b^{8}-48b^{6}p-3b^{4}p^2=-3b^{4}(64b^{4}+16b^2p+p^2)=-3b^{4}(8b^2+p)^2\)
4. \(-16s^{21}+25s^{5}=-s^{5}(16s^{16}-25)=-s^{5}(4s^8+5)(4s^8-5)\)
5. \(9b^{8}-49b^{2}=b^{2}(9b^{6}-49)=b^{2}(3b^3+7)(3b^3-7)\)
6. \(-9y^{7}+y^{5}=-y^{5}(9y^{2}-1)=-y^{5}(3y+1)(3y-1)\)
7. \(5y^{6}-50y^{5}+125y^{4}=5y^{4}(y^2-10y+25)=5y^{4}(y-5)^2\)
8. \(-75b^{4}-90b^{3}-27b^{2}=-3b^{2}(25b^{2}+30b+9)=-3b^{2}(5b+3)^2\)
9. \(y^{7}-10y^{6}+25y^{5}=y^{5}(y^2-10y+25)=y^{5}(y-5)^2\)
10. \(25a^{14}-70a^{9}y+49a^{4}y^2=a^{4}(25a^{10}-70a^5y+49y^2)=a^{4}(5a^5-7y)^2\)
11. \(108p^{7}-147p^{5}=3p^{5}(36p^{2}-49)=3p^{5}(6p+7)(6p-7)\)
12. \(-216b^{11}+360b^{8}y-150b^{5}y^2=-6b^{5}(36b^{6}-60b^3y+25y^2)=-6b^{5}(6b^3-5y)^2\)