Ontbinden in factoren (2)

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

1. \(-b^{7}-8b^{6}-16b^{5}\)
2. \(-98a^{15}-112a^{10}-32a^{5}\)
3. \(-150a^{5}+96a^{3}\)
4. \(-54p^{8}-144p^{6}-96p^{4}\)
5. \(96x^{4}+240x^{3}+150x^{2}\)
6. \(-6y^{5}+96y^{3}\)
7. \(2b^{7}-36b^{6}+162b^{5}\)
8. \(25x^{13}-40x^{9}+16x^{5}\)
9. \(-80a^{19}+125a^{3}\)
10. \(-180y^{6}+5y^{4}\)
11. \(5a^{6}-40a^{5}+80a^{4}\)
12. \(a^{7}-49a^{5}\)

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

Verbetersleutel

1. \(-b^{7}-8b^{6}-16b^{5}=-b^{5}(b^2+8b+16)=-b^{5}(b+4)^2\)
2. \(-98a^{15}-112a^{10}-32a^{5}=-2a^{5}(49a^{10}+56a^5+16)=-2a^{5}(7a^5+4)^2\)
3. \(-150a^{5}+96a^{3}=-6a^{3}(25a^{2}-16)=-6a^{3}(5a+4)(5a-4)\)
4. \(-54p^{8}-144p^{6}-96p^{4}=-6p^{4}(9p^{4}+24p^2+16)=-6p^{4}(3p^2+4)^2\)
5. \(96x^{4}+240x^{3}+150x^{2}=6x^{2}(16x^{2}+40x+25)=6x^{2}(4x+5)^2\)
6. \(-6y^{5}+96y^{3}=-6y^{3}(y^2-16)=-6y^{3}(y-4)(y+4)\)
7. \(2b^{7}-36b^{6}+162b^{5}=2b^{5}(b^2-18b+81)=2b^{5}(b-9)^2\)
8. \(25x^{13}-40x^{9}+16x^{5}=x^{5}(25x^{8}-40x^4+16)=x^{5}(5x^4-4)^2\)
9. \(-80a^{19}+125a^{3}=-5a^{3}(16a^{16}-25)=-5a^{3}(4a^8+5)(4a^8-5)\)
10. \(-180y^{6}+5y^{4}=-5y^{4}(36y^{2}-1)=-5y^{4}(6y+1)(6y-1)\)
11. \(5a^{6}-40a^{5}+80a^{4}=5a^{4}(a^2-8a+16)=5a^{4}(a-4)^2\)
12. \(a^{7}-49a^{5}=a^{5}(a^2-49)=a^{5}(a-7)(a+7)\)