Ontbinden in factoren (2)

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

1. \(80q^{4}-45q^{2}\)
2. \(45p^{6}-80p^{4}\)
3. \(-5p^{7}+20p^{6}-20p^{5}\)
4. \(-125q^{7}+245q^{5}\)
5. \(6s^{5}+24s^{4}+24s^{3}\)
6. \(3x^{4}-192x^{2}\)
7. \(-9b^{10}-24b^{6}x-16b^{2}x^2\)
8. \(96q^{12}-150q^{2}\)
9. \(216p^{4}-360p^{3}+150p^{2}\)
10. \(-5y^{5}+125y^{3}\)
11. \(20a^{5}-45a^{3}\)
12. \(-294q^{9}+504q^{6}s-216q^{3}s^2\)

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

Verbetersleutel

1. \(80q^{4}-45q^{2}=5q^{2}(16q^{2}-9)=5q^{2}(4q+3)(4q-3)\)
2. \(45p^{6}-80p^{4}=5p^{4}(9p^{2}-16)=5p^{4}(3p+4)(3p-4)\)
3. \(-5p^{7}+20p^{6}-20p^{5}=-5p^{5}(p^2-4p+4)=-5p^{5}(p-2)^2\)
4. \(-125q^{7}+245q^{5}=-5q^{5}(25q^{2}-49)=-5q^{5}(5q+7)(5q-7)\)
5. \(6s^{5}+24s^{4}+24s^{3}=6s^{3}(s^2+4s+4)=6s^{3}(s+2)^2\)
6. \(3x^{4}-192x^{2}=3x^{2}(x^2-64)=3x^{2}(x-8)(x+8)\)
7. \(-9b^{10}-24b^{6}x-16b^{2}x^2=-b^{2}(9b^{8}+24b^4x+16x^2)=-b^{2}(3b^4+4x)^2\)
8. \(96q^{12}-150q^{2}=6q^{2}(16q^{10}-25)=6q^{2}(4q^5+5)(4q^5-5)\)
9. \(216p^{4}-360p^{3}+150p^{2}=6p^{2}(36p^{2}-60p+25)=6p^{2}(6p-5)^2\)
10. \(-5y^{5}+125y^{3}=-5y^{3}(y^2-25)=-5y^{3}(y+5)(y-5)\)
11. \(20a^{5}-45a^{3}=5a^{3}(4a^{2}-9)=5a^{3}(2a+3)(2a-3)\)
12. \(-294q^{9}+504q^{6}s-216q^{3}s^2=-6q^{3}(49q^{6}-84q^3s+36s^2)=-6q^{3}(7q^3-6s)^2\)