Ontbinden in factoren (2)

Hoofdmenu Eentje per keer  🖨

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

1. \(108p^{6}-75p^{4}\)
2. \(-180y^{5}+300y^{4}-125y^{3}\)
3. \(9x^{6}+24x^{5}+16x^{4}\)
4. \(-2x^{5}-8x^{4}-8x^{3}\)
5. \(3y^{6}-192y^{4}\)
6. \(-54s^{6}+6s^{4}\)
7. \(-125q^{13}+100q^{9}-20q^{5}\)
8. \(-6a^{6}+84a^{5}-294a^{4}\)
9. \(50q^{12}+80q^{8}+32q^{4}\)
10. \(16a^{7}-9a^{5}\)
11. \(6s^{4}-150s^{2}\)
12. \(-6q^{5}+36q^{4}-54q^{3}\)

---

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

Verbetersleutel

1. \(108p^{6}-75p^{4}=3p^{4}(36p^{2}-25)=3p^{4}(6p+5)(6p-5)\)
2. \(-180y^{5}+300y^{4}-125y^{3}=-5y^{3}(36y^{2}-60y+25)=-5y^{3}(6y-5)^2\)
3. \(9x^{6}+24x^{5}+16x^{4}=x^{4}(9x^{2}+24x+16)=x^{4}(3x+4)^2\)
4. \(-2x^{5}-8x^{4}-8x^{3}=-2x^{3}(x^2+4x+4)=-2x^{3}(x+2)^2\)
5. \(3y^{6}-192y^{4}=3y^{4}(y^2-64)=3y^{4}(y-8)(y+8)\)
6. \(-54s^{6}+6s^{4}=-6s^{4}(9s^{2}-1)=-6s^{4}(3s+1)(3s-1)\)
7. \(-125q^{13}+100q^{9}-20q^{5}=-5q^{5}(25q^{8}-20q^4+4)=-5q^{5}(5q^4-2)^2\)
8. \(-6a^{6}+84a^{5}-294a^{4}=-6a^{4}(a^2-14a+49)=-6a^{4}(a-7)^2\)
9. \(50q^{12}+80q^{8}+32q^{4}=2q^{4}(25q^{8}+40q^4+16)=2q^{4}(5q^4+4)^2\)
10. \(16a^{7}-9a^{5}=a^{5}(16a^{2}-9)=a^{5}(4a+3)(4a-3)\)
11. \(6s^{4}-150s^{2}=6s^{2}(s^2-25)=6s^{2}(s-5)(s+5)\)
12. \(-6q^{5}+36q^{4}-54q^{3}=-6q^{3}(q^2-6q+9)=-6q^{3}(q-3)^2\)