Ontbinden in factoren (2)

Hoofdmenu Eentje per keer  🖨

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

1. \(9q^{13}+6q^{8}+q^{3}\)
2. \(-5q^{7}+5q^{5}\)
3. \(-216a^{11}+360a^{7}-150a^{3}\)
4. \(98b^{6}-252b^{5}+162b^{4}\)
5. \(-x^{6}+4x^{4}\)
6. \(45p^{19}-80p^{3}\)
7. \(-32b^{10}-48b^{7}y-18b^{4}y^2\)
8. \(32b^{11}+16b^{8}+2b^{5}\)
9. \(-49p^{6}+42p^{4}s-9p^{2}s^2\)
10. \(3q^{6}-75q^{4}\)
11. \(-45b^{4}-30b^{3}-5b^{2}\)
12. \(-20q^{7}+5q^{5}\)

---

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

Verbetersleutel

1. \(9q^{13}+6q^{8}+q^{3}=q^{3}(9q^{10}+6q^5+1)=q^{3}(3q^5+1)^2\)
2. \(-5q^{7}+5q^{5}=-5q^{5}(q^2-1)=-5q^{5}(q-1)(q+1)\)
3. \(-216a^{11}+360a^{7}-150a^{3}=-6a^{3}(36a^{8}-60a^4+25)=-6a^{3}(6a^4-5)^2\)
4. \(98b^{6}-252b^{5}+162b^{4}=2b^{4}(49b^{2}-126b+81)=2b^{4}(7b-9)^2\)
5. \(-x^{6}+4x^{4}=-x^{4}(x^2-4)=-x^{4}(x+2)(x-2)\)
6. \(45p^{19}-80p^{3}=5p^{3}(9p^{16}-16)=5p^{3}(3p^8+4)(3p^8-4)\)
7. \(-32b^{10}-48b^{7}y-18b^{4}y^2=-2b^{4}(16b^{6}+24b^3y+9y^2)=-2b^{4}(4b^3+3y)^2\)
8. \(32b^{11}+16b^{8}+2b^{5}=2b^{5}(16b^{6}+8b^3+1)=2b^{5}(4b^3+1)^2\)
9. \(-49p^{6}+42p^{4}s-9p^{2}s^2=-p^{2}(49p^{4}-42p^2s+9s^2)=-p^{2}(7p^2-3s)^2\)
10. \(3q^{6}-75q^{4}=3q^{4}(q^2-25)=3q^{4}(q-5)(q+5)\)
11. \(-45b^{4}-30b^{3}-5b^{2}=-5b^{2}(9b^{2}+6b+1)=-5b^{2}(3b+1)^2\)
12. \(-20q^{7}+5q^{5}=-5q^{5}(4q^{2}-1)=-5q^{5}(2q+1)(2q-1)\)