Ontbinden in factoren (2)

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

1. \(25b^{5}-40b^{4}+16b^{3}\)
2. \(150s^{6}-540s^{5}+486s^{4}\)
3. \(3p^{4}+30p^{3}+75p^{2}\)
4. \(27b^{6}-3b^{4}\)
5. \(54x^{6}-6x^{4}\)
6. \(-16x^{13}+x^{3}\)
7. \(-2b^{4}+50b^{2}\)
8. \(-245q^{7}-280q^{6}-80q^{5}\)
9. \(-25q^{13}+16q^{5}\)
10. \(-6q^{5}-108q^{4}-486q^{3}\)
11. \(125p^{4}+350p^{3}+245p^{2}\)
12. \(-18s^{6}+8s^{4}\)

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

Verbetersleutel

1. \(25b^{5}-40b^{4}+16b^{3}=b^{3}(25b^{2}-40b+16)=b^{3}(5b-4)^2\)
2. \(150s^{6}-540s^{5}+486s^{4}=6s^{4}(25s^{2}-90s+81)=6s^{4}(5s-9)^2\)
3. \(3p^{4}+30p^{3}+75p^{2}=3p^{2}(p^2+10p+25)=3p^{2}(p+5)^2\)
4. \(27b^{6}-3b^{4}=3b^{4}(9b^{2}-1)=3b^{4}(3b+1)(3b-1)\)
5. \(54x^{6}-6x^{4}=6x^{4}(9x^{2}-1)=6x^{4}(3x+1)(3x-1)\)
6. \(-16x^{13}+x^{3}=-x^{3}(16x^{10}-1)=-x^{3}(4x^5+1)(4x^5-1)\)
7. \(-2b^{4}+50b^{2}=-2b^{2}(b^2-25)=-2b^{2}(b-5)(b+5)\)
8. \(-245q^{7}-280q^{6}-80q^{5}=-5q^{5}(49q^{2}+56q+16)=-5q^{5}(7q+4)^2\)
9. \(-25q^{13}+16q^{5}=-q^{5}(25q^{8}-16)=-q^{5}(5q^4+4)(5q^4-4)\)
10. \(-6q^{5}-108q^{4}-486q^{3}=-6q^{3}(q^2+18q+81)=-6q^{3}(q+9)^2\)
11. \(125p^{4}+350p^{3}+245p^{2}=5p^{2}(25p^{2}+70p+49)=5p^{2}(5p+7)^2\)
12. \(-18s^{6}+8s^{4}=-2s^{4}(9s^{2}-4)=-2s^{4}(3s+2)(3s-2)\)