Ontbinden in factoren (2)

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

1. \(2a^{7}-8a^{5}\)
2. \(-5s^{4}+5s^{2}\)
3. \(80a^{16}-125a^{4}\)
4. \(-98y^{14}+168y^{9}-72y^{4}\)
5. \(-192b^{14}-144b^{9}-27b^{4}\)
6. \(3q^{6}-27q^{4}\)
7. \(27p^{11}-48p^{3}\)
8. \(16q^{4}-24q^{3}+9q^{2}\)
9. \(8x^{6}-18x^{4}\)
10. \(-5q^{4}+180q^{2}\)
11. \(96x^{10}-144x^{6}+54x^{2}\)
12. \(-36p^{11}+25p^{3}\)

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

Verbetersleutel

1. \(2a^{7}-8a^{5}=2a^{5}(a^2-4)=2a^{5}(a+2)(a-2)\)
2. \(-5s^{4}+5s^{2}=-5s^{2}(s^2-1)=-5s^{2}(s+1)(s-1)\)
3. \(80a^{16}-125a^{4}=5a^{4}(16a^{12}-25)=5a^{4}(4a^6+5)(4a^6-5)\)
4. \(-98y^{14}+168y^{9}-72y^{4}=-2y^{4}(49y^{10}-84y^5+36)=-2y^{4}(7y^5-6)^2\)
5. \(-192b^{14}-144b^{9}-27b^{4}=-3b^{4}(64b^{10}+48b^5+9)=-3b^{4}(8b^5+3)^2\)
6. \(3q^{6}-27q^{4}=3q^{4}(q^2-9)=3q^{4}(q-3)(q+3)\)
7. \(27p^{11}-48p^{3}=3p^{3}(9p^{8}-16)=3p^{3}(3p^4+4)(3p^4-4)\)
8. \(16q^{4}-24q^{3}+9q^{2}=q^{2}(16q^{2}-24q+9)=q^{2}(4q-3)^2\)
9. \(8x^{6}-18x^{4}=2x^{4}(4x^{2}-9)=2x^{4}(2x+3)(2x-3)\)
10. \(-5q^{4}+180q^{2}=-5q^{2}(q^2-36)=-5q^{2}(q-6)(q+6)\)
11. \(96x^{10}-144x^{6}+54x^{2}=6x^{2}(16x^{8}-24x^4+9)=6x^{2}(4x^4-3)^2\)
12. \(-36p^{11}+25p^{3}=-p^{3}(36p^{8}-25)=-p^{3}(6p^4+5)(6p^4-5)\)