Ontbinden in factoren (2)

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

1. \(216x^{11}-360x^{8}+150x^{5}\)
2. \(-5p^{6}-40p^{5}-80p^{4}\)
3. \(-25a^{9}-30a^{7}y-9a^{5}y^2\)
4. \(-a^{4}-4a^{3}-4a^{2}\)
5. \(-5p^{6}+50p^{5}-125p^{4}\)
6. \(-180q^{6}-60q^{5}-5q^{4}\)
7. \(192s^{11}-336s^{7}y+147s^{3}y^2\)
8. \(25s^{11}-40s^{8}x+16s^{5}x^2\)
9. \(-108b^{5}+180b^{4}-75b^{3}\)
10. \(-6b^{5}+384b^{3}\)
11. \(-54y^{9}+180y^{6}-150y^{3}\)
12. \(-48x^{5}-72x^{4}-27x^{3}\)

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

Verbetersleutel

1. \(216x^{11}-360x^{8}+150x^{5}=6x^{5}(36x^{6}-60x^3+25)=6x^{5}(6x^3-5)^2\)
2. \(-5p^{6}-40p^{5}-80p^{4}=-5p^{4}(p^2+8p+16)=-5p^{4}(p+4)^2\)
3. \(-25a^{9}-30a^{7}y-9a^{5}y^2=-a^{5}(25a^{4}+30a^2y+9y^2)=-a^{5}(5a^2+3y)^2\)
4. \(-a^{4}-4a^{3}-4a^{2}=-a^{2}(a^2+4a+4)=-a^{2}(a+2)^2\)
5. \(-5p^{6}+50p^{5}-125p^{4}=-5p^{4}(p^2-10p+25)=-5p^{4}(p-5)^2\)
6. \(-180q^{6}-60q^{5}-5q^{4}=-5q^{4}(36q^{2}+12q+1)=-5q^{4}(6q+1)^2\)
7. \(192s^{11}-336s^{7}y+147s^{3}y^2=3s^{3}(64s^{8}-112s^4y+49y^2)=3s^{3}(8s^4-7y)^2\)
8. \(25s^{11}-40s^{8}x+16s^{5}x^2=s^{5}(25s^{6}-40s^3x+16x^2)=s^{5}(5s^3-4x)^2\)
9. \(-108b^{5}+180b^{4}-75b^{3}=-3b^{3}(36b^{2}-60b+25)=-3b^{3}(6b-5)^2\)
10. \(-6b^{5}+384b^{3}=-6b^{3}(b^2-64)=-6b^{3}(b+8)(b-8)\)
11. \(-54y^{9}+180y^{6}-150y^{3}=-6y^{3}(9y^{6}-30y^3+25)=-6y^{3}(3y^3-5)^2\)
12. \(-48x^{5}-72x^{4}-27x^{3}=-3x^{3}(16x^{2}+24x+9)=-3x^{3}(4x+3)^2\)