Ontbinden in factoren (2)

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

1. \(-48q^{9}-24q^{6}-3q^{3}\)
2. \(-216b^{11}-72b^{8}-6b^{5}\)
3. \(20q^{4}+20q^{3}+5q^{2}\)
4. \(2s^{4}-50s^{2}\)
5. \(12b^{8}+12b^{6}+3b^{4}\)
6. \(-80s^{13}+125s^{5}\)
7. \(-80a^{6}-40a^{5}-5a^{4}\)
8. \(-25y^{15}+y^{3}\)
9. \(-6a^{4}+48a^{3}-96a^{2}\)
10. \(27b^{5}+18b^{4}+3b^{3}\)
11. \(80q^{6}-5q^{4}\)
12. \(45p^{4}-125p^{2}\)

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

Verbetersleutel

1. \(-48q^{9}-24q^{6}-3q^{3}=-3q^{3}(16q^{6}+8q^3+1)=-3q^{3}(4q^3+1)^2\)
2. \(-216b^{11}-72b^{8}-6b^{5}=-6b^{5}(36b^{6}+12b^3+1)=-6b^{5}(6b^3+1)^2\)
3. \(20q^{4}+20q^{3}+5q^{2}=5q^{2}(4q^{2}+4q+1)=5q^{2}(2q+1)^2\)
4. \(2s^{4}-50s^{2}=2s^{2}(s^2-25)=2s^{2}(s+5)(s-5)\)
5. \(12b^{8}+12b^{6}+3b^{4}=3b^{4}(4b^{4}+4b^2+1)=3b^{4}(2b^2+1)^2\)
6. \(-80s^{13}+125s^{5}=-5s^{5}(16s^{8}-25)=-5s^{5}(4s^4+5)(4s^4-5)\)
7. \(-80a^{6}-40a^{5}-5a^{4}=-5a^{4}(16a^{2}+8a+1)=-5a^{4}(4a+1)^2\)
8. \(-25y^{15}+y^{3}=-y^{3}(25y^{12}-1)=-y^{3}(5y^6+1)(5y^6-1)\)
9. \(-6a^{4}+48a^{3}-96a^{2}=-6a^{2}(a^2-8a+16)=-6a^{2}(a-4)^2\)
10. \(27b^{5}+18b^{4}+3b^{3}=3b^{3}(9b^{2}+6b+1)=3b^{3}(3b+1)^2\)
11. \(80q^{6}-5q^{4}=5q^{4}(16q^{2}-1)=5q^{4}(4q+1)(4q-1)\)
12. \(45p^{4}-125p^{2}=5p^{2}(9p^{2}-25)=5p^{2}(3p+5)(3p-5)\)