Ontbinden in factoren (2)

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

1. \(320s^{9}+400s^{6}+125s^{3}\)
2. \(125p^{17}-320p^{3}\)
3. \(80q^{8}+200q^{6}s+125q^{4}s^2\)
4. \(75b^{8}+120b^{6}x+48b^{4}x^2\)
5. \(80x^{6}-5x^{4}\)
6. \(24p^{9}+120p^{7}s+150p^{5}s^2\)
7. \(-5y^{5}+20y^{3}\)
8. \(27b^{4}-147b^{2}\)
9. \(2b^{7}-128b^{5}\)
10. \(75b^{7}-192b^{5}\)
11. \(-12a^{13}+27a^{5}\)
12. \(98b^{7}-84b^{6}+18b^{5}\)

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

Verbetersleutel

1. \(320s^{9}+400s^{6}+125s^{3}=5s^{3}(64s^{6}+80s^3+25)=5s^{3}(8s^3+5)^2\)
2. \(125p^{17}-320p^{3}=5p^{3}(25p^{14}-64)=5p^{3}(5p^7+8)(5p^7-8)\)
3. \(80q^{8}+200q^{6}s+125q^{4}s^2=5q^{4}(16q^{4}+40q^2s+25s^2)=5q^{4}(4q^2+5s)^2\)
4. \(75b^{8}+120b^{6}x+48b^{4}x^2=3b^{4}(25b^{4}+40b^2x+16x^2)=3b^{4}(5b^2+4x)^2\)
5. \(80x^{6}-5x^{4}=5x^{4}(16x^{2}-1)=5x^{4}(4x+1)(4x-1)\)
6. \(24p^{9}+120p^{7}s+150p^{5}s^2=6p^{5}(4p^{4}+20p^2s+25s^2)=6p^{5}(2p^2+5s)^2\)
7. \(-5y^{5}+20y^{3}=-5y^{3}(y^2-4)=-5y^{3}(y-2)(y+2)\)
8. \(27b^{4}-147b^{2}=3b^{2}(9b^{2}-49)=3b^{2}(3b+7)(3b-7)\)
9. \(2b^{7}-128b^{5}=2b^{5}(b^2-64)=2b^{5}(b+8)(b-8)\)
10. \(75b^{7}-192b^{5}=3b^{5}(25b^{2}-64)=3b^{5}(5b+8)(5b-8)\)
11. \(-12a^{13}+27a^{5}=-3a^{5}(4a^{8}-9)=-3a^{5}(2a^4+3)(2a^4-3)\)
12. \(98b^{7}-84b^{6}+18b^{5}=2b^{5}(49b^{2}-42b+9)=2b^{5}(7b-3)^2\)