Ontbinden in factoren (2)

Hoofdmenu Eentje per keer  🖨

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

1. \(3b^{4}+36b^{3}+108b^{2}\)
2. \(125x^{4}-20x^{2}\)
3. \(x^{6}-8x^{5}+16x^{4}\)
4. \(6x^{5}-384x^{3}\)
5. \(-216b^{12}-72b^{8}p-6b^{4}p^2\)
6. \(27b^{6}-90b^{5}+75b^{4}\)
7. \(-180a^{14}+125a^{4}\)
8. \(5y^{4}+90y^{3}+405y^{2}\)
9. \(245a^{4}-210a^{3}+45a^{2}\)
10. \(24s^{12}+24s^{7}+6s^{2}\)
11. \(-216p^{15}-360p^{10}-150p^{5}\)
12. \(96s^{5}-150s^{3}\)

---

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

Verbetersleutel

1. \(3b^{4}+36b^{3}+108b^{2}=3b^{2}(b^2+12b+36)=3b^{2}(b+6)^2\)
2. \(125x^{4}-20x^{2}=5x^{2}(25x^{2}-4)=5x^{2}(5x+2)(5x-2)\)
3. \(x^{6}-8x^{5}+16x^{4}=x^{4}(x^2-8x+16)=x^{4}(x-4)^2\)
4. \(6x^{5}-384x^{3}=6x^{3}(x^2-64)=6x^{3}(x-8)(x+8)\)
5. \(-216b^{12}-72b^{8}p-6b^{4}p^2=-6b^{4}(36b^{8}+12b^4p+p^2)=-6b^{4}(6b^4+p)^2\)
6. \(27b^{6}-90b^{5}+75b^{4}=3b^{4}(9b^{2}-30b+25)=3b^{4}(3b-5)^2\)
7. \(-180a^{14}+125a^{4}=-5a^{4}(36a^{10}-25)=-5a^{4}(6a^5+5)(6a^5-5)\)
8. \(5y^{4}+90y^{3}+405y^{2}=5y^{2}(y^2+18y+81)=5y^{2}(y+9)^2\)
9. \(245a^{4}-210a^{3}+45a^{2}=5a^{2}(49a^{2}-42a+9)=5a^{2}(7a-3)^2\)
10. \(24s^{12}+24s^{7}+6s^{2}=6s^{2}(4s^{10}+4s^5+1)=6s^{2}(2s^5+1)^2\)
11. \(-216p^{15}-360p^{10}-150p^{5}=-6p^{5}(36p^{10}+60p^5+25)=-6p^{5}(6p^5+5)^2\)
12. \(96s^{5}-150s^{3}=6s^{3}(16s^{2}-25)=6s^{3}(4s+5)(4s-5)\)