Ontbinden in factoren (2)

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

1. \(2y^{7}+20y^{6}+50y^{5}\)
2. \(54b^{9}+180b^{7}s+150b^{5}s^2\)
3. \(216a^{6}-6a^{4}\)
4. \(-108q^{10}-180q^{6}-75q^{2}\)
5. \(-3y^{6}+54y^{5}-243y^{4}\)
6. \(-27b^{6}+75b^{4}\)
7. \(4q^{14}-25q^{4}\)
8. \(4b^{10}+4b^{6}+b^{2}\)
9. \(-5q^{6}-30q^{5}-45q^{4}\)
10. \(4a^{7}+4a^{6}+a^{5}\)
11. \(8p^{14}+8p^{9}y+2p^{4}y^2\)
12. \(80b^{8}-5b^{4}\)

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

Verbetersleutel

1. \(2y^{7}+20y^{6}+50y^{5}=2y^{5}(y^2+10y+25)=2y^{5}(y+5)^2\)
2. \(54b^{9}+180b^{7}s+150b^{5}s^2=6b^{5}(9b^{4}+30b^2s+25s^2)=6b^{5}(3b^2+5s)^2\)
3. \(216a^{6}-6a^{4}=6a^{4}(36a^{2}-1)=6a^{4}(6a+1)(6a-1)\)
4. \(-108q^{10}-180q^{6}-75q^{2}=-3q^{2}(36q^{8}+60q^4+25)=-3q^{2}(6q^4+5)^2\)
5. \(-3y^{6}+54y^{5}-243y^{4}=-3y^{4}(y^2-18y+81)=-3y^{4}(y-9)^2\)
6. \(-27b^{6}+75b^{4}=-3b^{4}(9b^{2}-25)=-3b^{4}(3b+5)(3b-5)\)
7. \(4q^{14}-25q^{4}=q^{4}(4q^{10}-25)=q^{4}(2q^5+5)(2q^5-5)\)
8. \(4b^{10}+4b^{6}+b^{2}=b^{2}(4b^{8}+4b^4+1)=b^{2}(2b^4+1)^2\)
9. \(-5q^{6}-30q^{5}-45q^{4}=-5q^{4}(q^2+6q+9)=-5q^{4}(q+3)^2\)
10. \(4a^{7}+4a^{6}+a^{5}=a^{5}(4a^{2}+4a+1)=a^{5}(2a+1)^2\)
11. \(8p^{14}+8p^{9}y+2p^{4}y^2=2p^{4}(4p^{10}+4p^5y+y^2)=2p^{4}(2p^5+y)^2\)
12. \(80b^{8}-5b^{4}=5b^{4}(16b^{4}-1)=5b^{4}(4b^2+1)(4b^2-1)\)