Ontbinden in factoren (2)

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

1. \(125q^{10}-200q^{7}+80q^{4}\)
2. \(s^{7}-64s^{5}\)
3. \(24q^{5}-54q^{3}\)
4. \(-294y^{6}-420y^{5}-150y^{4}\)
5. \(-75p^{6}+120p^{4}x-48p^{2}x^2\)
6. \(147b^{4}-252b^{3}+108b^{2}\)
7. \(-320y^{6}+560y^{5}-245y^{4}\)
8. \(245p^{8}+140p^{5}+20p^{2}\)
9. \(80b^{4}+40b^{3}+5b^{2}\)
10. \(-27q^{7}+12q^{5}\)
11. \(20s^{8}+20s^{5}x+5s^{2}x^2\)
12. \(-80a^{7}+125a^{5}\)

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

Verbetersleutel

1. \(125q^{10}-200q^{7}+80q^{4}=5q^{4}(25q^{6}-40q^3+16)=5q^{4}(5q^3-4)^2\)
2. \(s^{7}-64s^{5}=s^{5}(s^2-64)=s^{5}(s-8)(s+8)\)
3. \(24q^{5}-54q^{3}=6q^{3}(4q^{2}-9)=6q^{3}(2q+3)(2q-3)\)
4. \(-294y^{6}-420y^{5}-150y^{4}=-6y^{4}(49y^{2}+70y+25)=-6y^{4}(7y+5)^2\)
5. \(-75p^{6}+120p^{4}x-48p^{2}x^2=-3p^{2}(25p^{4}-40p^2x+16x^2)=-3p^{2}(5p^2-4x)^2\)
6. \(147b^{4}-252b^{3}+108b^{2}=3b^{2}(49b^{2}-84b+36)=3b^{2}(7b-6)^2\)
7. \(-320y^{6}+560y^{5}-245y^{4}=-5y^{4}(64y^{2}-112y+49)=-5y^{4}(8y-7)^2\)
8. \(245p^{8}+140p^{5}+20p^{2}=5p^{2}(49p^{6}+28p^3+4)=5p^{2}(7p^3+2)^2\)
9. \(80b^{4}+40b^{3}+5b^{2}=5b^{2}(16b^{2}+8b+1)=5b^{2}(4b+1)^2\)
10. \(-27q^{7}+12q^{5}=-3q^{5}(9q^{2}-4)=-3q^{5}(3q+2)(3q-2)\)
11. \(20s^{8}+20s^{5}x+5s^{2}x^2=5s^{2}(4s^{6}+4s^3x+x^2)=5s^{2}(2s^3+x)^2\)
12. \(-80a^{7}+125a^{5}=-5a^{5}(16a^{2}-25)=-5a^{5}(4a+5)(4a-5)\)