Ontbinden in factoren (2)

Hoofdmenu Eentje per keer  🖨

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

1. \(20a^{15}+20a^{10}s+5a^{5}s^2\)
2. \(-x^{5}+4x^{4}-4x^{3}\)
3. \(27a^{10}+18a^{6}x+3a^{2}x^2\)
4. \(6s^{4}+12s^{3}+6s^{2}\)
5. \(36x^{6}-60x^{5}+25x^{4}\)
6. \(-3p^{6}+12p^{4}\)
7. \(9b^{14}-12b^{9}+4b^{4}\)
8. \(5q^{4}-10q^{3}+5q^{2}\)
9. \(27q^{11}-48q^{5}\)
10. \(-128a^{15}-32a^{10}-2a^{5}\)
11. \(-20s^{21}+5s^{5}\)
12. \(-6q^{7}-84q^{6}-294q^{5}\)

---

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

Verbetersleutel

1. \(20a^{15}+20a^{10}s+5a^{5}s^2=5a^{5}(4a^{10}+4a^5s+s^2)=5a^{5}(2a^5+s)^2\)
2. \(-x^{5}+4x^{4}-4x^{3}=-x^{3}(x^2-4x+4)=-x^{3}(x-2)^2\)
3. \(27a^{10}+18a^{6}x+3a^{2}x^2=3a^{2}(9a^{8}+6a^4x+x^2)=3a^{2}(3a^4+x)^2\)
4. \(6s^{4}+12s^{3}+6s^{2}=6s^{2}(s^2+2s+1)=6s^{2}(s+1)^2\)
5. \(36x^{6}-60x^{5}+25x^{4}=x^{4}(36x^{2}-60x+25)=x^{4}(6x-5)^2\)
6. \(-3p^{6}+12p^{4}=-3p^{4}(p^2-4)=-3p^{4}(p-2)(p+2)\)
7. \(9b^{14}-12b^{9}+4b^{4}=b^{4}(9b^{10}-12b^5+4)=b^{4}(3b^5-2)^2\)
8. \(5q^{4}-10q^{3}+5q^{2}=5q^{2}(q^2-2q+1)=5q^{2}(q-1)^2\)
9. \(27q^{11}-48q^{5}=3q^{5}(9q^{6}-16)=3q^{5}(3q^3+4)(3q^3-4)\)
10. \(-128a^{15}-32a^{10}-2a^{5}=-2a^{5}(64a^{10}+16a^5+1)=-2a^{5}(8a^5+1)^2\)
11. \(-20s^{21}+5s^{5}=-5s^{5}(4s^{16}-1)=-5s^{5}(2s^8+1)(2s^8-1)\)
12. \(-6q^{7}-84q^{6}-294q^{5}=-6q^{5}(q^2+14q+49)=-6q^{5}(q+7)^2\)