Ontbinden in factoren (2)

Hoofdmenu Eentje per keer  🖨

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

1. \(-108a^{6}+180a^{4}q-75a^{2}q^2\)
2. \(18a^{6}-50a^{4}\)
3. \(-6a^{4}+72a^{3}-216a^{2}\)
4. \(-2s^{6}+32s^{4}\)
5. \(32p^{7}-48p^{5}x+18p^{3}x^2\)
6. \(192p^{13}+48p^{8}y+3p^{3}y^2\)
7. \(-5y^{5}+245y^{3}\)
8. \(2a^{4}-24a^{3}+72a^{2}\)
9. \(-8b^{14}-8b^{9}q-2b^{4}q^2\)
10. \(-18a^{5}+50a^{3}\)
11. \(2x^{6}-50x^{4}\)
12. \(18p^{8}+12p^{6}+2p^{4}\)

---

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

Verbetersleutel

1. \(-108a^{6}+180a^{4}q-75a^{2}q^2=-3a^{2}(36a^{4}-60a^2q+25q^2)=-3a^{2}(6a^2-5q)^2\)
2. \(18a^{6}-50a^{4}=2a^{4}(9a^{2}-25)=2a^{4}(3a+5)(3a-5)\)
3. \(-6a^{4}+72a^{3}-216a^{2}=-6a^{2}(a^2-12a+36)=-6a^{2}(a-6)^2\)
4. \(-2s^{6}+32s^{4}=-2s^{4}(s^2-16)=-2s^{4}(s+4)(s-4)\)
5. \(32p^{7}-48p^{5}x+18p^{3}x^2=2p^{3}(16p^{4}-24p^2x+9x^2)=2p^{3}(4p^2-3x)^2\)
6. \(192p^{13}+48p^{8}y+3p^{3}y^2=3p^{3}(64p^{10}+16p^5y+y^2)=3p^{3}(8p^5+y)^2\)
7. \(-5y^{5}+245y^{3}=-5y^{3}(y^2-49)=-5y^{3}(y+7)(y-7)\)
8. \(2a^{4}-24a^{3}+72a^{2}=2a^{2}(a^2-12a+36)=2a^{2}(a-6)^2\)
9. \(-8b^{14}-8b^{9}q-2b^{4}q^2=-2b^{4}(4b^{10}+4b^5q+q^2)=-2b^{4}(2b^5+q)^2\)
10. \(-18a^{5}+50a^{3}=-2a^{3}(9a^{2}-25)=-2a^{3}(3a+5)(3a-5)\)
11. \(2x^{6}-50x^{4}=2x^{4}(x^2-25)=2x^{4}(x+5)(x-5)\)
12. \(18p^{8}+12p^{6}+2p^{4}=2p^{4}(9p^{4}+6p^2+1)=2p^{4}(3p^2+1)^2\)