Ontbinden in factoren (2)

Hoofdmenu Eentje per keer  🖨

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

1. \(-9a^{12}-6a^{8}-a^{4}\)
2. \(20b^{5}-45b^{3}\)
3. \(-2b^{4}-28b^{3}-98b^{2}\)
4. \(-12q^{6}-60q^{4}-75q^{2}\)
5. \(36y^{4}-49y^{2}\)
6. \(320b^{5}-560b^{4}+245b^{3}\)
7. \(p^{5}-9p^{3}\)
8. \(x^{6}+2x^{5}+x^{4}\)
9. \(-125p^{8}-200p^{5}q-80p^{2}q^2\)
10. \(2b^{6}-8b^{4}\)
11. \(80y^{9}+200y^{6}+125y^{3}\)
12. \(3q^{7}-48q^{5}\)

---

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

Verbetersleutel

1. \(-9a^{12}-6a^{8}-a^{4}=-a^{4}(9a^{8}+6a^4+1)=-a^{4}(3a^4+1)^2\)
2. \(20b^{5}-45b^{3}=5b^{3}(4b^{2}-9)=5b^{3}(2b+3)(2b-3)\)
3. \(-2b^{4}-28b^{3}-98b^{2}=-2b^{2}(b^2+14b+49)=-2b^{2}(b+7)^2\)
4. \(-12q^{6}-60q^{4}-75q^{2}=-3q^{2}(4q^{4}+20q^2+25)=-3q^{2}(2q^2+5)^2\)
5. \(36y^{4}-49y^{2}=y^{2}(36y^{2}-49)=y^{2}(6y+7)(6y-7)\)
6. \(320b^{5}-560b^{4}+245b^{3}=5b^{3}(64b^{2}-112b+49)=5b^{3}(8b-7)^2\)
7. \(p^{5}-9p^{3}=p^{3}(p^2-9)=p^{3}(p+3)(p-3)\)
8. \(x^{6}+2x^{5}+x^{4}=x^{4}(x^2+2x+1)=x^{4}(x+1)^2\)
9. \(-125p^{8}-200p^{5}q-80p^{2}q^2=-5p^{2}(25p^{6}+40p^3q+16q^2)=-5p^{2}(5p^3+4q)^2\)
10. \(2b^{6}-8b^{4}=2b^{4}(b^2-4)=2b^{4}(b+2)(b-2)\)
11. \(80y^{9}+200y^{6}+125y^{3}=5y^{3}(16y^{6}+40y^3+25)=5y^{3}(4y^3+5)^2\)
12. \(3q^{7}-48q^{5}=3q^{5}(q^2-16)=3q^{5}(q+4)(q-4)\)