Ontbinden in factoren (2)

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

1. \(216b^{6}+72b^{4}+6b^{2}\)
2. \(-98x^{10}-168x^{6}-72x^{2}\)
3. \(-75a^{8}-180a^{5}-108a^{2}\)
4. \(-54x^{7}-180x^{5}y-150x^{3}y^2\)
5. \(-216p^{7}-72p^{5}s-6p^{3}s^2\)
6. \(216p^{12}-6p^{2}\)
7. \(-49b^{11}+28b^{8}y-4b^{5}y^2\)
8. \(8s^{14}+8s^{9}+2s^{4}\)
9. \(384y^{6}+96y^{4}+6y^{2}\)
10. \(150b^{4}-96b^{2}\)
11. \(-3b^{4}+30b^{3}-75b^{2}\)
12. \(8b^{8}+24b^{5}+18b^{2}\)

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

Verbetersleutel

1. \(216b^{6}+72b^{4}+6b^{2}=6b^{2}(36b^{4}+12b^2+1)=6b^{2}(6b^2+1)^2\)
2. \(-98x^{10}-168x^{6}-72x^{2}=-2x^{2}(49x^{8}+84x^4+36)=-2x^{2}(7x^4+6)^2\)
3. \(-75a^{8}-180a^{5}-108a^{2}=-3a^{2}(25a^{6}+60a^3+36)=-3a^{2}(5a^3+6)^2\)
4. \(-54x^{7}-180x^{5}y-150x^{3}y^2=-6x^{3}(9x^{4}+30x^2y+25y^2)=-6x^{3}(3x^2+5y)^2\)
5. \(-216p^{7}-72p^{5}s-6p^{3}s^2=-6p^{3}(36p^{4}+12p^2s+s^2)=-6p^{3}(6p^2+s)^2\)
6. \(216p^{12}-6p^{2}=6p^{2}(36p^{10}-1)=6p^{2}(6p^5+1)(6p^5-1)\)
7. \(-49b^{11}+28b^{8}y-4b^{5}y^2=-b^{5}(49b^{6}-28b^3y+4y^2)=-b^{5}(7b^3-2y)^2\)
8. \(8s^{14}+8s^{9}+2s^{4}=2s^{4}(4s^{10}+4s^5+1)=2s^{4}(2s^5+1)^2\)
9. \(384y^{6}+96y^{4}+6y^{2}=6y^{2}(64y^{4}+16y^2+1)=6y^{2}(8y^2+1)^2\)
10. \(150b^{4}-96b^{2}=6b^{2}(25b^{2}-16)=6b^{2}(5b+4)(5b-4)\)
11. \(-3b^{4}+30b^{3}-75b^{2}=-3b^{2}(b^2-10b+25)=-3b^{2}(b-5)^2\)
12. \(8b^{8}+24b^{5}+18b^{2}=2b^{2}(4b^{6}+12b^3+9)=2b^{2}(2b^3+3)^2\)