Ontbinden in factoren (2)

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

1. \(54a^{7}-6a^{5}\)
2. \(45p^{12}+120p^{8}+80p^{4}\)
3. \(-54a^{10}-36a^{6}-6a^{2}\)
4. \(-6x^{4}+150x^{2}\)
5. \(80b^{5}+40b^{4}+5b^{3}\)
6. \(-320s^{7}-80s^{6}-5s^{5}\)
7. \(5s^{6}-245s^{4}\)
8. \(36b^{4}+84b^{3}+49b^{2}\)
9. \(-5y^{6}+180y^{4}\)
10. \(54a^{18}-6a^{2}\)
11. \(-54a^{7}-180a^{6}-150a^{5}\)
12. \(150b^{6}-540b^{5}+486b^{4}\)

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

Verbetersleutel

1. \(54a^{7}-6a^{5}=6a^{5}(9a^{2}-1)=6a^{5}(3a+1)(3a-1)\)
2. \(45p^{12}+120p^{8}+80p^{4}=5p^{4}(9p^{8}+24p^4+16)=5p^{4}(3p^4+4)^2\)
3. \(-54a^{10}-36a^{6}-6a^{2}=-6a^{2}(9a^{8}+6a^4+1)=-6a^{2}(3a^4+1)^2\)
4. \(-6x^{4}+150x^{2}=-6x^{2}(x^2-25)=-6x^{2}(x-5)(x+5)\)
5. \(80b^{5}+40b^{4}+5b^{3}=5b^{3}(16b^{2}+8b+1)=5b^{3}(4b+1)^2\)
6. \(-320s^{7}-80s^{6}-5s^{5}=-5s^{5}(64s^{2}+16s+1)=-5s^{5}(8s+1)^2\)
7. \(5s^{6}-245s^{4}=5s^{4}(s^2-49)=5s^{4}(s+7)(s-7)\)
8. \(36b^{4}+84b^{3}+49b^{2}=b^{2}(36b^{2}+84b+49)=b^{2}(6b+7)^2\)
9. \(-5y^{6}+180y^{4}=-5y^{4}(y^2-36)=-5y^{4}(y+6)(y-6)\)
10. \(54a^{18}-6a^{2}=6a^{2}(9a^{16}-1)=6a^{2}(3a^8+1)(3a^8-1)\)
11. \(-54a^{7}-180a^{6}-150a^{5}=-6a^{5}(9a^{2}+30a+25)=-6a^{5}(3a+5)^2\)
12. \(150b^{6}-540b^{5}+486b^{4}=6b^{4}(25b^{2}-90b+81)=6b^{4}(5b-9)^2\)