Ontbinden in factoren (2)

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

1. \(108s^{12}+180s^{8}+75s^{4}\)
2. \(-9b^{5}+16b^{3}\)
3. \(150a^{6}+120a^{4}q+24a^{2}q^2\)
4. \(3s^{6}-147s^{4}\)
5. \(-48x^{7}+27x^{5}\)
6. \(20b^{11}+20b^{7}+5b^{3}\)
7. \(-75p^{9}-120p^{6}q-48p^{3}q^2\)
8. \(108q^{12}-180q^{7}+75q^{2}\)
9. \(b^{6}-9b^{4}\)
10. \(-108s^{4}+147s^{2}\)
11. \(-125a^{6}+450a^{5}-405a^{4}\)
12. \(294a^{6}-504a^{4}x+216a^{2}x^2\)

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

Verbetersleutel

1. \(108s^{12}+180s^{8}+75s^{4}=3s^{4}(36s^{8}+60s^4+25)=3s^{4}(6s^4+5)^2\)
2. \(-9b^{5}+16b^{3}=-b^{3}(9b^{2}-16)=-b^{3}(3b+4)(3b-4)\)
3. \(150a^{6}+120a^{4}q+24a^{2}q^2=6a^{2}(25a^{4}+20a^2q+4q^2)=6a^{2}(5a^2+2q)^2\)
4. \(3s^{6}-147s^{4}=3s^{4}(s^2-49)=3s^{4}(s+7)(s-7)\)
5. \(-48x^{7}+27x^{5}=-3x^{5}(16x^{2}-9)=-3x^{5}(4x+3)(4x-3)\)
6. \(20b^{11}+20b^{7}+5b^{3}=5b^{3}(4b^{8}+4b^4+1)=5b^{3}(2b^4+1)^2\)
7. \(-75p^{9}-120p^{6}q-48p^{3}q^2=-3p^{3}(25p^{6}+40p^3q+16q^2)=-3p^{3}(5p^3+4q)^2\)
8. \(108q^{12}-180q^{7}+75q^{2}=3q^{2}(36q^{10}-60q^5+25)=3q^{2}(6q^5-5)^2\)
9. \(b^{6}-9b^{4}=b^{4}(b^2-9)=b^{4}(b-3)(b+3)\)
10. \(-108s^{4}+147s^{2}=-3s^{2}(36s^{2}-49)=-3s^{2}(6s+7)(6s-7)\)
11. \(-125a^{6}+450a^{5}-405a^{4}=-5a^{4}(25a^{2}-90a+81)=-5a^{4}(5a-9)^2\)
12. \(294a^{6}-504a^{4}x+216a^{2}x^2=6a^{2}(49a^{4}-84a^2x+36x^2)=6a^{2}(7a^2-6x)^2\)