Ontbinden in factoren (2)

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

1. \(-2p^{6}+50p^{4}\)
2. \(25q^{12}+10q^{7}s+q^{2}s^2\)
3. \(-8b^{17}+98b^{5}\)
4. \(8p^{13}+8p^{9}s+2p^{5}s^2\)
5. \(147p^{12}-84p^{8}+12p^{4}\)
6. \(12b^{5}-3b^{3}\)
7. \(50b^{4}-72b^{2}\)
8. \(-20x^{5}-20x^{4}-5x^{3}\)
9. \(32a^{5}-50a^{3}\)
10. \(-3a^{6}+54a^{5}-243a^{4}\)
11. \(-96p^{12}-144p^{8}q-54p^{4}q^2\)
12. \(96b^{21}-150b^{5}\)

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

Verbetersleutel

1. \(-2p^{6}+50p^{4}=-2p^{4}(p^2-25)=-2p^{4}(p+5)(p-5)\)
2. \(25q^{12}+10q^{7}s+q^{2}s^2=q^{2}(25q^{10}+10q^5s+s^2)=q^{2}(5q^5+s)^2\)
3. \(-8b^{17}+98b^{5}=-2b^{5}(4b^{12}-49)=-2b^{5}(2b^6+7)(2b^6-7)\)
4. \(8p^{13}+8p^{9}s+2p^{5}s^2=2p^{5}(4p^{8}+4p^4s+s^2)=2p^{5}(2p^4+s)^2\)
5. \(147p^{12}-84p^{8}+12p^{4}=3p^{4}(49p^{8}-28p^4+4)=3p^{4}(7p^4-2)^2\)
6. \(12b^{5}-3b^{3}=3b^{3}(4b^{2}-1)=3b^{3}(2b+1)(2b-1)\)
7. \(50b^{4}-72b^{2}=2b^{2}(25b^{2}-36)=2b^{2}(5b+6)(5b-6)\)
8. \(-20x^{5}-20x^{4}-5x^{3}=-5x^{3}(4x^{2}+4x+1)=-5x^{3}(2x+1)^2\)
9. \(32a^{5}-50a^{3}=2a^{3}(16a^{2}-25)=2a^{3}(4a+5)(4a-5)\)
10. \(-3a^{6}+54a^{5}-243a^{4}=-3a^{4}(a^2-18a+81)=-3a^{4}(a-9)^2\)
11. \(-96p^{12}-144p^{8}q-54p^{4}q^2=-6p^{4}(16p^{8}+24p^4q+9q^2)=-6p^{4}(4p^4+3q)^2\)
12. \(96b^{21}-150b^{5}=6b^{5}(16b^{16}-25)=6b^{5}(4b^8+5)(4b^8-5)\)