Ontbinden in factoren (2)

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

1. \(3p^{7}-27p^{5}\)
2. \(216p^{9}-150p^{5}\)
3. \(-b^{7}+b^{5}\)
4. \(-48s^{7}+75s^{5}\)
5. \(s^{4}-25s^{2}\)
6. \(-75s^{5}+60s^{4}-12s^{3}\)
7. \(-27b^{7}-18b^{5}p-3b^{3}p^2\)
8. \(-80s^{14}+120s^{9}x-45s^{4}x^2\)
9. \(-64b^{8}+112b^{6}q-49b^{4}q^2\)
10. \(-125p^{6}+20p^{4}\)
11. \(-45s^{4}+60s^{3}-20s^{2}\)
12. \(50q^{4}-2q^{2}\)

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

Verbetersleutel

1. \(3p^{7}-27p^{5}=3p^{5}(p^2-9)=3p^{5}(p+3)(p-3)\)
2. \(216p^{9}-150p^{5}=6p^{5}(36p^{4}-25)=6p^{5}(6p^2+5)(6p^2-5)\)
3. \(-b^{7}+b^{5}=-b^{5}(b^2-1)=-b^{5}(b-1)(b+1)\)
4. \(-48s^{7}+75s^{5}=-3s^{5}(16s^{2}-25)=-3s^{5}(4s+5)(4s-5)\)
5. \(s^{4}-25s^{2}=s^{2}(s^2-25)=s^{2}(s-5)(s+5)\)
6. \(-75s^{5}+60s^{4}-12s^{3}=-3s^{3}(25s^{2}-20s+4)=-3s^{3}(5s-2)^2\)
7. \(-27b^{7}-18b^{5}p-3b^{3}p^2=-3b^{3}(9b^{4}+6b^2p+p^2)=-3b^{3}(3b^2+p)^2\)
8. \(-80s^{14}+120s^{9}x-45s^{4}x^2=-5s^{4}(16s^{10}-24s^5x+9x^2)=-5s^{4}(4s^5-3x)^2\)
9. \(-64b^{8}+112b^{6}q-49b^{4}q^2=-b^{4}(64b^{4}-112b^2q+49q^2)=-b^{4}(8b^2-7q)^2\)
10. \(-125p^{6}+20p^{4}=-5p^{4}(25p^{2}-4)=-5p^{4}(5p+2)(5p-2)\)
11. \(-45s^{4}+60s^{3}-20s^{2}=-5s^{2}(9s^{2}-12s+4)=-5s^{2}(3s-2)^2\)
12. \(50q^{4}-2q^{2}=2q^{2}(25q^{2}-1)=2q^{2}(5q+1)(5q-1)\)