Ontbinden in factoren (2)

Hoofdmenu Eentje per keer  🖨

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

1. \(-245a^{12}-70a^{8}y-5a^{4}y^2\)
2. \(-45a^{14}+5a^{4}\)
3. \(25y^{5}+80y^{4}+64y^{3}\)
4. \(3q^{7}+30q^{6}+75q^{5}\)
5. \(-6p^{7}+216p^{5}\)
6. \(b^{7}+12b^{6}+36b^{5}\)
7. \(64y^{6}+16y^{4}+y^{2}\)
8. \(-18b^{12}+60b^{8}y-50b^{4}y^2\)
9. \(50p^{6}-98p^{4}\)
10. \(128s^{13}+32s^{9}y+2s^{5}y^2\)
11. \(9p^{14}-12p^{9}q+4p^{4}q^2\)
12. \(-25x^{4}+40x^{3}-16x^{2}\)

---

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

Verbetersleutel

1. \(-245a^{12}-70a^{8}y-5a^{4}y^2=-5a^{4}(49a^{8}+14a^4y+y^2)=-5a^{4}(7a^4+y)^2\)
2. \(-45a^{14}+5a^{4}=-5a^{4}(9a^{10}-1)=-5a^{4}(3a^5+1)(3a^5-1)\)
3. \(25y^{5}+80y^{4}+64y^{3}=y^{3}(25y^{2}+80y+64)=y^{3}(5y+8)^2\)
4. \(3q^{7}+30q^{6}+75q^{5}=3q^{5}(q^2+10q+25)=3q^{5}(q+5)^2\)
5. \(-6p^{7}+216p^{5}=-6p^{5}(p^2-36)=-6p^{5}(p-6)(p+6)\)
6. \(b^{7}+12b^{6}+36b^{5}=b^{5}(b^2+12b+36)=b^{5}(b+6)^2\)
7. \(64y^{6}+16y^{4}+y^{2}=y^{2}(64y^{4}+16y^2+1)=y^{2}(8y^2+1)^2\)
8. \(-18b^{12}+60b^{8}y-50b^{4}y^2=-2b^{4}(9b^{8}-30b^4y+25y^2)=-2b^{4}(3b^4-5y)^2\)
9. \(50p^{6}-98p^{4}=2p^{4}(25p^{2}-49)=2p^{4}(5p+7)(5p-7)\)
10. \(128s^{13}+32s^{9}y+2s^{5}y^2=2s^{5}(64s^{8}+16s^4y+y^2)=2s^{5}(8s^4+y)^2\)
11. \(9p^{14}-12p^{9}q+4p^{4}q^2=p^{4}(9p^{10}-12p^5q+4q^2)=p^{4}(3p^5-2q)^2\)
12. \(-25x^{4}+40x^{3}-16x^{2}=-x^{2}(25x^{2}-40x+16)=-x^{2}(5x-4)^2\)