Ontbinden in factoren (2)

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

1. \(48a^{4}+120a^{3}+75a^{2}\)
2. \(-8a^{11}-24a^{8}q-18a^{5}q^2\)
3. \(2q^{4}-16q^{3}+32q^{2}\)
4. \(-s^{4}-4s^{3}-4s^{2}\)
5. \(-27b^{9}+90b^{6}p-75b^{3}p^2\)
6. \(6y^{7}-216y^{5}\)
7. \(-y^{7}+25y^{5}\)
8. \(-27a^{14}+36a^{9}-12a^{4}\)
9. \(-2b^{5}-8b^{4}-8b^{3}\)
10. \(2x^{7}+20x^{6}+50x^{5}\)
11. \(-3x^{4}+27x^{2}\)
12. \(-320p^{7}+560p^{5}-245p^{3}\)

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

Verbetersleutel

1. \(48a^{4}+120a^{3}+75a^{2}=3a^{2}(16a^{2}+40a+25)=3a^{2}(4a+5)^2\)
2. \(-8a^{11}-24a^{8}q-18a^{5}q^2=-2a^{5}(4a^{6}+12a^3q+9q^2)=-2a^{5}(2a^3+3q)^2\)
3. \(2q^{4}-16q^{3}+32q^{2}=2q^{2}(q^2-8q+16)=2q^{2}(q-4)^2\)
4. \(-s^{4}-4s^{3}-4s^{2}=-s^{2}(s^2+4s+4)=-s^{2}(s+2)^2\)
5. \(-27b^{9}+90b^{6}p-75b^{3}p^2=-3b^{3}(9b^{6}-30b^3p+25p^2)=-3b^{3}(3b^3-5p)^2\)
6. \(6y^{7}-216y^{5}=6y^{5}(y^2-36)=6y^{5}(y+6)(y-6)\)
7. \(-y^{7}+25y^{5}=-y^{5}(y^2-25)=-y^{5}(y-5)(y+5)\)
8. \(-27a^{14}+36a^{9}-12a^{4}=-3a^{4}(9a^{10}-12a^5+4)=-3a^{4}(3a^5-2)^2\)
9. \(-2b^{5}-8b^{4}-8b^{3}=-2b^{3}(b^2+4b+4)=-2b^{3}(b+2)^2\)
10. \(2x^{7}+20x^{6}+50x^{5}=2x^{5}(x^2+10x+25)=2x^{5}(x+5)^2\)
11. \(-3x^{4}+27x^{2}=-3x^{2}(x^2-9)=-3x^{2}(x+3)(x-3)\)
12. \(-320p^{7}+560p^{5}-245p^{3}=-5p^{3}(64p^{4}-112p^2+49)=-5p^{3}(8p^2-7)^2\)