Ontbinden in factoren (2)

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

1. \(5q^{7}-125q^{5}\)
2. \(-320q^{5}-80q^{4}-5q^{3}\)
3. \(-24s^{5}-24s^{4}-6s^{3}\)
4. \(-3b^{6}+48b^{4}\)
5. \(147b^{10}-252b^{6}p+108b^{2}p^2\)
6. \(2s^{6}+16s^{5}+32s^{4}\)
7. \(9b^{6}+6b^{5}+b^{4}\)
8. \(-6s^{6}-72s^{5}-216s^{4}\)
9. \(-16y^{8}+y^{2}\)
10. \(-p^{4}+64p^{2}\)
11. \(6p^{4}+60p^{3}+150p^{2}\)
12. \(8b^{6}-50b^{4}\)

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

Verbetersleutel

1. \(5q^{7}-125q^{5}=5q^{5}(q^2-25)=5q^{5}(q-5)(q+5)\)
2. \(-320q^{5}-80q^{4}-5q^{3}=-5q^{3}(64q^{2}+16q+1)=-5q^{3}(8q+1)^2\)
3. \(-24s^{5}-24s^{4}-6s^{3}=-6s^{3}(4s^{2}+4s+1)=-6s^{3}(2s+1)^2\)
4. \(-3b^{6}+48b^{4}=-3b^{4}(b^2-16)=-3b^{4}(b+4)(b-4)\)
5. \(147b^{10}-252b^{6}p+108b^{2}p^2=3b^{2}(49b^{8}-84b^4p+36p^2)=3b^{2}(7b^4-6p)^2\)
6. \(2s^{6}+16s^{5}+32s^{4}=2s^{4}(s^2+8s+16)=2s^{4}(s+4)^2\)
7. \(9b^{6}+6b^{5}+b^{4}=b^{4}(9b^{2}+6b+1)=b^{4}(3b+1)^2\)
8. \(-6s^{6}-72s^{5}-216s^{4}=-6s^{4}(s^2+12s+36)=-6s^{4}(s+6)^2\)
9. \(-16y^{8}+y^{2}=-y^{2}(16y^{6}-1)=-y^{2}(4y^3+1)(4y^3-1)\)
10. \(-p^{4}+64p^{2}=-p^{2}(p^2-64)=-p^{2}(p+8)(p-8)\)
11. \(6p^{4}+60p^{3}+150p^{2}=6p^{2}(p^2+10p+25)=6p^{2}(p+5)^2\)
12. \(8b^{6}-50b^{4}=2b^{4}(4b^{2}-25)=2b^{4}(2b+5)(2b-5)\)