Ontbinden in factoren (2)

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

1. \(-25b^{4}-80b^{3}-64b^{2}\)
2. \(-80q^{8}+245q^{4}\)
3. \(3s^{5}-27s^{3}\)
4. \(5q^{7}-180q^{5}\)
5. \(20p^{10}+100p^{6}x+125p^{2}x^2\)
6. \(125x^{5}+100x^{4}+20x^{3}\)
7. \(y^{4}-9y^{2}\)
8. \(-5s^{6}+40s^{5}-80s^{4}\)
9. \(-216a^{7}+150a^{5}\)
10. \(4s^{9}-s^{3}\)
11. \(2x^{6}-128x^{4}\)
12. \(-s^{7}+18s^{6}-81s^{5}\)

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

Verbetersleutel

1. \(-25b^{4}-80b^{3}-64b^{2}=-b^{2}(25b^{2}+80b+64)=-b^{2}(5b+8)^2\)
2. \(-80q^{8}+245q^{4}=-5q^{4}(16q^{4}-49)=-5q^{4}(4q^2+7)(4q^2-7)\)
3. \(3s^{5}-27s^{3}=3s^{3}(s^2-9)=3s^{3}(s+3)(s-3)\)
4. \(5q^{7}-180q^{5}=5q^{5}(q^2-36)=5q^{5}(q+6)(q-6)\)
5. \(20p^{10}+100p^{6}x+125p^{2}x^2=5p^{2}(4p^{8}+20p^4x+25x^2)=5p^{2}(2p^4+5x)^2\)
6. \(125x^{5}+100x^{4}+20x^{3}=5x^{3}(25x^{2}+20x+4)=5x^{3}(5x+2)^2\)
7. \(y^{4}-9y^{2}=y^{2}(y^2-9)=y^{2}(y-3)(y+3)\)
8. \(-5s^{6}+40s^{5}-80s^{4}=-5s^{4}(s^2-8s+16)=-5s^{4}(s-4)^2\)
9. \(-216a^{7}+150a^{5}=-6a^{5}(36a^{2}-25)=-6a^{5}(6a+5)(6a-5)\)
10. \(4s^{9}-s^{3}=s^{3}(4s^{6}-1)=s^{3}(2s^3+1)(2s^3-1)\)
11. \(2x^{6}-128x^{4}=2x^{4}(x^2-64)=2x^{4}(x-8)(x+8)\)
12. \(-s^{7}+18s^{6}-81s^{5}=-s^{5}(s^2-18s+81)=-s^{5}(s-9)^2\)