Ontbinden in factoren (2)

Hoofdmenu Eentje per keer  🖨

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

1. \(-16x^{12}+9x^{4}\)
2. \(a^{6}+8a^{5}+16a^{4}\)
3. \(-3p^{4}+192p^{2}\)
4. \(50b^{6}-72b^{4}\)
5. \(-s^{4}+2s^{3}-s^{2}\)
6. \(50p^{13}-80p^{9}x+32p^{5}x^2\)
7. \(80b^{12}-120b^{8}q+45b^{4}q^2\)
8. \(-108a^{7}-36a^{6}-3a^{5}\)
9. \(-4x^{13}-4x^{8}y-x^{3}y^2\)
10. \(36b^{12}+12b^{7}x+b^{2}x^2\)
11. \(54y^{6}-288y^{5}+384y^{4}\)
12. \(3q^{7}-18q^{6}+27q^{5}\)

---

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

Verbetersleutel

1. \(-16x^{12}+9x^{4}=-x^{4}(16x^{8}-9)=-x^{4}(4x^4+3)(4x^4-3)\)
2. \(a^{6}+8a^{5}+16a^{4}=a^{4}(a^2+8a+16)=a^{4}(a+4)^2\)
3. \(-3p^{4}+192p^{2}=-3p^{2}(p^2-64)=-3p^{2}(p-8)(p+8)\)
4. \(50b^{6}-72b^{4}=2b^{4}(25b^{2}-36)=2b^{4}(5b+6)(5b-6)\)
5. \(-s^{4}+2s^{3}-s^{2}=-s^{2}(s^2-2s+1)=-s^{2}(s-1)^2\)
6. \(50p^{13}-80p^{9}x+32p^{5}x^2=2p^{5}(25p^{8}-40p^4x+16x^2)=2p^{5}(5p^4-4x)^2\)
7. \(80b^{12}-120b^{8}q+45b^{4}q^2=5b^{4}(16b^{8}-24b^4q+9q^2)=5b^{4}(4b^4-3q)^2\)
8. \(-108a^{7}-36a^{6}-3a^{5}=-3a^{5}(36a^{2}+12a+1)=-3a^{5}(6a+1)^2\)
9. \(-4x^{13}-4x^{8}y-x^{3}y^2=-x^{3}(4x^{10}+4x^5y+y^2)=-x^{3}(2x^5+y)^2\)
10. \(36b^{12}+12b^{7}x+b^{2}x^2=b^{2}(36b^{10}+12b^5x+x^2)=b^{2}(6b^5+x)^2\)
11. \(54y^{6}-288y^{5}+384y^{4}=6y^{4}(9y^{2}-48y+64)=6y^{4}(3y-8)^2\)
12. \(3q^{7}-18q^{6}+27q^{5}=3q^{5}(q^2-6q+9)=3q^{5}(q-3)^2\)