Ontbinden in factoren (2)

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

1. \(s^{7}-4s^{6}+4s^{5}\)
2. \(-25q^{7}+16q^{5}\)
3. \(147a^{9}-126a^{6}b+27a^{3}b^2\)
4. \(-6a^{5}+384a^{3}\)
5. \(-25y^{5}+70y^{4}-49y^{3}\)
6. \(-2a^{6}+32a^{4}\)
7. \(8a^{14}-2a^{4}\)
8. \(-36q^{5}+60q^{4}-25q^{3}\)
9. \(-72p^{6}-24p^{5}-2p^{4}\)
10. \(-5y^{6}-60y^{5}-180y^{4}\)
11. \(4q^{13}+4q^{9}s+q^{5}s^2\)
12. \(125b^{8}+300b^{6}+180b^{4}\)

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

Verbetersleutel

1. \(s^{7}-4s^{6}+4s^{5}=s^{5}(s^2-4s+4)=s^{5}(s-2)^2\)
2. \(-25q^{7}+16q^{5}=-q^{5}(25q^{2}-16)=-q^{5}(5q+4)(5q-4)\)
3. \(147a^{9}-126a^{6}b+27a^{3}b^2=3a^{3}(49a^{6}-42a^3b+9b^2)=3a^{3}(7a^3-3b)^2\)
4. \(-6a^{5}+384a^{3}=-6a^{3}(a^2-64)=-6a^{3}(a-8)(a+8)\)
5. \(-25y^{5}+70y^{4}-49y^{3}=-y^{3}(25y^{2}-70y+49)=-y^{3}(5y-7)^2\)
6. \(-2a^{6}+32a^{4}=-2a^{4}(a^2-16)=-2a^{4}(a-4)(a+4)\)
7. \(8a^{14}-2a^{4}=2a^{4}(4a^{10}-1)=2a^{4}(2a^5+1)(2a^5-1)\)
8. \(-36q^{5}+60q^{4}-25q^{3}=-q^{3}(36q^{2}-60q+25)=-q^{3}(6q-5)^2\)
9. \(-72p^{6}-24p^{5}-2p^{4}=-2p^{4}(36p^{2}+12p+1)=-2p^{4}(6p+1)^2\)
10. \(-5y^{6}-60y^{5}-180y^{4}=-5y^{4}(y^2+12y+36)=-5y^{4}(y+6)^2\)
11. \(4q^{13}+4q^{9}s+q^{5}s^2=q^{5}(4q^{8}+4q^4s+s^2)=q^{5}(2q^4+s)^2\)
12. \(125b^{8}+300b^{6}+180b^{4}=5b^{4}(25b^{4}+60b^2+36)=5b^{4}(5b^2+6)^2\)