Ontbinden in factoren (2)

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

1. \(-20p^{14}-20p^{9}-5p^{4}\)
2. \(-150a^{13}+216a^{5}\)
3. \(-5a^{7}+90a^{6}-405a^{5}\)
4. \(-54y^{5}+72y^{4}-24y^{3}\)
5. \(3y^{5}+48y^{4}+192y^{3}\)
6. \(y^{4}-64y^{2}\)
7. \(45b^{8}-150b^{5}y+125b^{2}y^2\)
8. \(54s^{13}-180s^{9}+150s^{5}\)
9. \(-20x^{6}-20x^{5}-5x^{4}\)
10. \(-18s^{9}+50s^{5}\)
11. \(75y^{8}-12y^{4}\)
12. \(-50q^{11}+8q^{3}\)

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

Verbetersleutel

1. \(-20p^{14}-20p^{9}-5p^{4}=-5p^{4}(4p^{10}+4p^5+1)=-5p^{4}(2p^5+1)^2\)
2. \(-150a^{13}+216a^{5}=-6a^{5}(25a^{8}-36)=-6a^{5}(5a^4+6)(5a^4-6)\)
3. \(-5a^{7}+90a^{6}-405a^{5}=-5a^{5}(a^2-18a+81)=-5a^{5}(a-9)^2\)
4. \(-54y^{5}+72y^{4}-24y^{3}=-6y^{3}(9y^{2}-12y+4)=-6y^{3}(3y-2)^2\)
5. \(3y^{5}+48y^{4}+192y^{3}=3y^{3}(y^2+16y+64)=3y^{3}(y+8)^2\)
6. \(y^{4}-64y^{2}=y^{2}(y^2-64)=y^{2}(y+8)(y-8)\)
7. \(45b^{8}-150b^{5}y+125b^{2}y^2=5b^{2}(9b^{6}-30b^3y+25y^2)=5b^{2}(3b^3-5y)^2\)
8. \(54s^{13}-180s^{9}+150s^{5}=6s^{5}(9s^{8}-30s^4+25)=6s^{5}(3s^4-5)^2\)
9. \(-20x^{6}-20x^{5}-5x^{4}=-5x^{4}(4x^{2}+4x+1)=-5x^{4}(2x+1)^2\)
10. \(-18s^{9}+50s^{5}=-2s^{5}(9s^{4}-25)=-2s^{5}(3s^2+5)(3s^2-5)\)
11. \(75y^{8}-12y^{4}=3y^{4}(25y^{4}-4)=3y^{4}(5y^2+2)(5y^2-2)\)
12. \(-50q^{11}+8q^{3}=-2q^{3}(25q^{8}-4)=-2q^{3}(5q^4+2)(5q^4-2)\)