Ontbinden in factoren (2)

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

1. \(3q^{7}-192q^{5}\)
2. \(216p^{6}-6p^{4}\)
3. \(18x^{6}-2x^{4}\)
4. \(245a^{9}-420a^{6}x+180a^{3}x^2\)
5. \(-s^{7}+16s^{5}\)
6. \(-54p^{6}+180p^{4}x-150p^{2}x^2\)
7. \(50a^{14}-18a^{2}\)
8. \(5a^{7}+30a^{6}+45a^{5}\)
9. \(-96p^{12}-48p^{7}y-6p^{2}y^2\)
10. \(-48p^{6}+168p^{4}-147p^{2}\)
11. \(-32x^{12}+50x^{2}\)
12. \(64y^{15}+16y^{10}+y^{5}\)

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

Verbetersleutel

1. \(3q^{7}-192q^{5}=3q^{5}(q^2-64)=3q^{5}(q-8)(q+8)\)
2. \(216p^{6}-6p^{4}=6p^{4}(36p^{2}-1)=6p^{4}(6p+1)(6p-1)\)
3. \(18x^{6}-2x^{4}=2x^{4}(9x^{2}-1)=2x^{4}(3x+1)(3x-1)\)
4. \(245a^{9}-420a^{6}x+180a^{3}x^2=5a^{3}(49a^{6}-84a^3x+36x^2)=5a^{3}(7a^3-6x)^2\)
5. \(-s^{7}+16s^{5}=-s^{5}(s^2-16)=-s^{5}(s-4)(s+4)\)
6. \(-54p^{6}+180p^{4}x-150p^{2}x^2=-6p^{2}(9p^{4}-30p^2x+25x^2)=-6p^{2}(3p^2-5x)^2\)
7. \(50a^{14}-18a^{2}=2a^{2}(25a^{12}-9)=2a^{2}(5a^6+3)(5a^6-3)\)
8. \(5a^{7}+30a^{6}+45a^{5}=5a^{5}(a^2+6a+9)=5a^{5}(a+3)^2\)
9. \(-96p^{12}-48p^{7}y-6p^{2}y^2=-6p^{2}(16p^{10}+8p^5y+y^2)=-6p^{2}(4p^5+y)^2\)
10. \(-48p^{6}+168p^{4}-147p^{2}=-3p^{2}(16p^{4}-56p^2+49)=-3p^{2}(4p^2-7)^2\)
11. \(-32x^{12}+50x^{2}=-2x^{2}(16x^{10}-25)=-2x^{2}(4x^5+5)(4x^5-5)\)
12. \(64y^{15}+16y^{10}+y^{5}=y^{5}(64y^{10}+16y^5+1)=y^{5}(8y^5+1)^2\)