Ontbinden in factoren (2)

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

1. \(216p^{11}-150p^{3}\)
2. \(12b^{4}-27b^{2}\)
3. \(5x^{7}-45x^{5}\)
4. \(-320a^{7}+560a^{6}-245a^{5}\)
5. \(24b^{13}+72b^{9}p+54b^{5}p^2\)
6. \(180s^{10}-245s^{2}\)
7. \(-49x^{5}+42x^{4}-9x^{3}\)
8. \(50p^{11}+120p^{7}+72p^{3}\)
9. \(-2b^{6}+16b^{5}-32b^{4}\)
10. \(25a^{9}+30a^{6}x+9a^{3}x^2\)
11. \(-108s^{14}-180s^{9}y-75s^{4}y^2\)
12. \(-49q^{8}-42q^{6}s-9q^{4}s^2\)

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

Verbetersleutel

1. \(216p^{11}-150p^{3}=6p^{3}(36p^{8}-25)=6p^{3}(6p^4+5)(6p^4-5)\)
2. \(12b^{4}-27b^{2}=3b^{2}(4b^{2}-9)=3b^{2}(2b+3)(2b-3)\)
3. \(5x^{7}-45x^{5}=5x^{5}(x^2-9)=5x^{5}(x+3)(x-3)\)
4. \(-320a^{7}+560a^{6}-245a^{5}=-5a^{5}(64a^{2}-112a+49)=-5a^{5}(8a-7)^2\)
5. \(24b^{13}+72b^{9}p+54b^{5}p^2=6b^{5}(4b^{8}+12b^4p+9p^2)=6b^{5}(2b^4+3p)^2\)
6. \(180s^{10}-245s^{2}=5s^{2}(36s^{8}-49)=5s^{2}(6s^4+7)(6s^4-7)\)
7. \(-49x^{5}+42x^{4}-9x^{3}=-x^{3}(49x^{2}-42x+9)=-x^{3}(7x-3)^2\)
8. \(50p^{11}+120p^{7}+72p^{3}=2p^{3}(25p^{8}+60p^4+36)=2p^{3}(5p^4+6)^2\)
9. \(-2b^{6}+16b^{5}-32b^{4}=-2b^{4}(b^2-8b+16)=-2b^{4}(b-4)^2\)
10. \(25a^{9}+30a^{6}x+9a^{3}x^2=a^{3}(25a^{6}+30a^3x+9x^2)=a^{3}(5a^3+3x)^2\)
11. \(-108s^{14}-180s^{9}y-75s^{4}y^2=-3s^{4}(36s^{10}+60s^5y+25y^2)=-3s^{4}(6s^5+5y)^2\)
12. \(-49q^{8}-42q^{6}s-9q^{4}s^2=-q^{4}(49q^{4}+42q^2s+9s^2)=-q^{4}(7q^2+3s)^2\)