Ontbinden in factoren (2)

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

1. \(s^{5}-36s^{3}\)
2. \(75b^{15}-120b^{10}+48b^{5}\)
3. \(245b^{9}+140b^{7}+20b^{5}\)
4. \(-16s^{6}-24s^{4}y-9s^{2}y^2\)
5. \(45s^{6}-245s^{4}\)
6. \(147s^{15}-126s^{10}x+27s^{5}x^2\)
7. \(384p^{13}+480p^{9}+150p^{5}\)
8. \(-48s^{9}-120s^{7}y-75s^{5}y^2\)
9. \(-x^{6}+64x^{4}\)
10. \(-25b^{17}+36b^{3}\)
11. \(50q^{7}+140q^{6}+98q^{5}\)
12. \(-6q^{4}+216q^{2}\)

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

Verbetersleutel

1. \(s^{5}-36s^{3}=s^{3}(s^2-36)=s^{3}(s+6)(s-6)\)
2. \(75b^{15}-120b^{10}+48b^{5}=3b^{5}(25b^{10}-40b^5+16)=3b^{5}(5b^5-4)^2\)
3. \(245b^{9}+140b^{7}+20b^{5}=5b^{5}(49b^{4}+28b^2+4)=5b^{5}(7b^2+2)^2\)
4. \(-16s^{6}-24s^{4}y-9s^{2}y^2=-s^{2}(16s^{4}+24s^2y+9y^2)=-s^{2}(4s^2+3y)^2\)
5. \(45s^{6}-245s^{4}=5s^{4}(9s^{2}-49)=5s^{4}(3s+7)(3s-7)\)
6. \(147s^{15}-126s^{10}x+27s^{5}x^2=3s^{5}(49s^{10}-42s^5x+9x^2)=3s^{5}(7s^5-3x)^2\)
7. \(384p^{13}+480p^{9}+150p^{5}=6p^{5}(64p^{8}+80p^4+25)=6p^{5}(8p^4+5)^2\)
8. \(-48s^{9}-120s^{7}y-75s^{5}y^2=-3s^{5}(16s^{4}+40s^2y+25y^2)=-3s^{5}(4s^2+5y)^2\)
9. \(-x^{6}+64x^{4}=-x^{4}(x^2-64)=-x^{4}(x-8)(x+8)\)
10. \(-25b^{17}+36b^{3}=-b^{3}(25b^{14}-36)=-b^{3}(5b^7+6)(5b^7-6)\)
11. \(50q^{7}+140q^{6}+98q^{5}=2q^{5}(25q^{2}+70q+49)=2q^{5}(5q+7)^2\)
12. \(-6q^{4}+216q^{2}=-6q^{2}(q^2-36)=-6q^{2}(q-6)(q+6)\)