Ontbinden in factoren (2)

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

1. \(-54p^{4}+6p^{2}\)
2. \(-25b^{17}+b^{5}\)
3. \(-49b^{5}-14b^{4}-b^{3}\)
4. \(4b^{5}+12b^{4}+9b^{3}\)
5. \(-80b^{8}-200b^{6}s-125b^{4}s^2\)
6. \(125b^{8}-100b^{6}q+20b^{4}q^2\)
7. \(96b^{5}+336b^{4}+294b^{3}\)
8. \(-8x^{9}+2x^{3}\)
9. \(50p^{12}-72p^{2}\)
10. \(54b^{6}+144b^{4}x+96b^{2}x^2\)
11. \(5b^{7}-5b^{5}\)
12. \(2q^{5}-128q^{3}\)

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

Verbetersleutel

1. \(-54p^{4}+6p^{2}=-6p^{2}(9p^{2}-1)=-6p^{2}(3p+1)(3p-1)\)
2. \(-25b^{17}+b^{5}=-b^{5}(25b^{12}-1)=-b^{5}(5b^6+1)(5b^6-1)\)
3. \(-49b^{5}-14b^{4}-b^{3}=-b^{3}(49b^{2}+14b+1)=-b^{3}(7b+1)^2\)
4. \(4b^{5}+12b^{4}+9b^{3}=b^{3}(4b^{2}+12b+9)=b^{3}(2b+3)^2\)
5. \(-80b^{8}-200b^{6}s-125b^{4}s^2=-5b^{4}(16b^{4}+40b^2s+25s^2)=-5b^{4}(4b^2+5s)^2\)
6. \(125b^{8}-100b^{6}q+20b^{4}q^2=5b^{4}(25b^{4}-20b^2q+4q^2)=5b^{4}(5b^2-2q)^2\)
7. \(96b^{5}+336b^{4}+294b^{3}=6b^{3}(16b^{2}+56b+49)=6b^{3}(4b+7)^2\)
8. \(-8x^{9}+2x^{3}=-2x^{3}(4x^{6}-1)=-2x^{3}(2x^3+1)(2x^3-1)\)
9. \(50p^{12}-72p^{2}=2p^{2}(25p^{10}-36)=2p^{2}(5p^5+6)(5p^5-6)\)
10. \(54b^{6}+144b^{4}x+96b^{2}x^2=6b^{2}(9b^{4}+24b^2x+16x^2)=6b^{2}(3b^2+4x)^2\)
11. \(5b^{7}-5b^{5}=5b^{5}(b^2-1)=5b^{5}(b-1)(b+1)\)
12. \(2q^{5}-128q^{3}=2q^{3}(q^2-64)=2q^{3}(q-8)(q+8)\)