Ontbinden in factoren (2)

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

1. \(-49a^{11}-28a^{8}-4a^{5}\)
2. \(-192b^{8}-48b^{5}-3b^{2}\)
3. \(-54p^{11}-36p^{7}y-6p^{3}y^2\)
4. \(5b^{5}-5b^{3}\)
5. \(216s^{17}-294s^{5}\)
6. \(-12x^{4}-12x^{3}-3x^{2}\)
7. \(-147x^{13}+84x^{8}-12x^{3}\)
8. \(98b^{10}-84b^{7}+18b^{4}\)
9. \(-6p^{7}-96p^{6}-384p^{5}\)
10. \(-80a^{12}-40a^{7}-5a^{2}\)
11. \(72x^{7}+24x^{5}+2x^{3}\)
12. \(-27x^{5}+147x^{3}\)

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

Verbetersleutel

1. \(-49a^{11}-28a^{8}-4a^{5}=-a^{5}(49a^{6}+28a^3+4)=-a^{5}(7a^3+2)^2\)
2. \(-192b^{8}-48b^{5}-3b^{2}=-3b^{2}(64b^{6}+16b^3+1)=-3b^{2}(8b^3+1)^2\)
3. \(-54p^{11}-36p^{7}y-6p^{3}y^2=-6p^{3}(9p^{8}+6p^4y+y^2)=-6p^{3}(3p^4+y)^2\)
4. \(5b^{5}-5b^{3}=5b^{3}(b^2-1)=5b^{3}(b+1)(b-1)\)
5. \(216s^{17}-294s^{5}=6s^{5}(36s^{12}-49)=6s^{5}(6s^6+7)(6s^6-7)\)
6. \(-12x^{4}-12x^{3}-3x^{2}=-3x^{2}(4x^{2}+4x+1)=-3x^{2}(2x+1)^2\)
7. \(-147x^{13}+84x^{8}-12x^{3}=-3x^{3}(49x^{10}-28x^5+4)=-3x^{3}(7x^5-2)^2\)
8. \(98b^{10}-84b^{7}+18b^{4}=2b^{4}(49b^{6}-42b^3+9)=2b^{4}(7b^3-3)^2\)
9. \(-6p^{7}-96p^{6}-384p^{5}=-6p^{5}(p^2+16p+64)=-6p^{5}(p+8)^2\)
10. \(-80a^{12}-40a^{7}-5a^{2}=-5a^{2}(16a^{10}+8a^5+1)=-5a^{2}(4a^5+1)^2\)
11. \(72x^{7}+24x^{5}+2x^{3}=2x^{3}(36x^{4}+12x^2+1)=2x^{3}(6x^2+1)^2\)
12. \(-27x^{5}+147x^{3}=-3x^{3}(9x^{2}-49)=-3x^{3}(3x+7)(3x-7)\)