Ontbinden in factoren (2)

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

1. \(-16a^{7}-24a^{5}y-9a^{3}y^2\)
2. \(6p^{6}+48p^{5}+96p^{4}\)
3. \(2y^{6}-32y^{4}\)
4. \(-2s^{7}+32s^{6}-128s^{5}\)
5. \(-125p^{21}+20p^{5}\)
6. \(192b^{4}+144b^{3}+27b^{2}\)
7. \(6p^{5}-150p^{3}\)
8. \(54q^{6}+252q^{5}+294q^{4}\)
9. \(-a^{5}+64a^{3}\)
10. \(-294b^{11}-420b^{8}y-150b^{5}y^2\)
11. \(125p^{12}-350p^{7}x+245p^{2}x^2\)
12. \(-5a^{7}+40a^{6}-80a^{5}\)

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

Verbetersleutel

1. \(-16a^{7}-24a^{5}y-9a^{3}y^2=-a^{3}(16a^{4}+24a^2y+9y^2)=-a^{3}(4a^2+3y)^2\)
2. \(6p^{6}+48p^{5}+96p^{4}=6p^{4}(p^2+8p+16)=6p^{4}(p+4)^2\)
3. \(2y^{6}-32y^{4}=2y^{4}(y^2-16)=2y^{4}(y+4)(y-4)\)
4. \(-2s^{7}+32s^{6}-128s^{5}=-2s^{5}(s^2-16s+64)=-2s^{5}(s-8)^2\)
5. \(-125p^{21}+20p^{5}=-5p^{5}(25p^{16}-4)=-5p^{5}(5p^8+2)(5p^8-2)\)
6. \(192b^{4}+144b^{3}+27b^{2}=3b^{2}(64b^{2}+48b+9)=3b^{2}(8b+3)^2\)
7. \(6p^{5}-150p^{3}=6p^{3}(p^2-25)=6p^{3}(p+5)(p-5)\)
8. \(54q^{6}+252q^{5}+294q^{4}=6q^{4}(9q^{2}+42q+49)=6q^{4}(3q+7)^2\)
9. \(-a^{5}+64a^{3}=-a^{3}(a^2-64)=-a^{3}(a+8)(a-8)\)
10. \(-294b^{11}-420b^{8}y-150b^{5}y^2=-6b^{5}(49b^{6}+70b^3y+25y^2)=-6b^{5}(7b^3+5y)^2\)
11. \(125p^{12}-350p^{7}x+245p^{2}x^2=5p^{2}(25p^{10}-70p^5x+49x^2)=5p^{2}(5p^5-7x)^2\)
12. \(-5a^{7}+40a^{6}-80a^{5}=-5a^{5}(a^2-8a+16)=-5a^{5}(a-4)^2\)