Ontbinden in factoren (2)

Hoofdmenu Eentje per keer  🖨

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

1. \(48b^{6}+72b^{4}y+27b^{2}y^2\)
2. \(4q^{10}+20q^{7}+25q^{4}\)
3. \(-y^{6}+6y^{5}-9y^{4}\)
4. \(-3x^{5}-24x^{4}-48x^{3}\)
5. \(-64p^{10}-80p^{6}-25p^{2}\)
6. \(49p^{11}+56p^{7}x+16p^{3}x^2\)
7. \(150p^{7}+480p^{6}+384p^{5}\)
8. \(-180a^{12}+300a^{8}-125a^{4}\)
9. \(-245x^{7}-560x^{6}-320x^{5}\)
10. \(-2x^{5}-24x^{4}-72x^{3}\)
11. \(9a^{7}-49a^{5}\)
12. \(-50x^{9}+40x^{7}-8x^{5}\)

---

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

Verbetersleutel

1. \(48b^{6}+72b^{4}y+27b^{2}y^2=3b^{2}(16b^{4}+24b^2y+9y^2)=3b^{2}(4b^2+3y)^2\)
2. \(4q^{10}+20q^{7}+25q^{4}=q^{4}(4q^{6}+20q^3+25)=q^{4}(2q^3+5)^2\)
3. \(-y^{6}+6y^{5}-9y^{4}=-y^{4}(y^2-6y+9)=-y^{4}(y-3)^2\)
4. \(-3x^{5}-24x^{4}-48x^{3}=-3x^{3}(x^2+8x+16)=-3x^{3}(x+4)^2\)
5. \(-64p^{10}-80p^{6}-25p^{2}=-p^{2}(64p^{8}+80p^4+25)=-p^{2}(8p^4+5)^2\)
6. \(49p^{11}+56p^{7}x+16p^{3}x^2=p^{3}(49p^{8}+56p^4x+16x^2)=p^{3}(7p^4+4x)^2\)
7. \(150p^{7}+480p^{6}+384p^{5}=6p^{5}(25p^{2}+80p+64)=6p^{5}(5p+8)^2\)
8. \(-180a^{12}+300a^{8}-125a^{4}=-5a^{4}(36a^{8}-60a^4+25)=-5a^{4}(6a^4-5)^2\)
9. \(-245x^{7}-560x^{6}-320x^{5}=-5x^{5}(49x^{2}+112x+64)=-5x^{5}(7x+8)^2\)
10. \(-2x^{5}-24x^{4}-72x^{3}=-2x^{3}(x^2+12x+36)=-2x^{3}(x+6)^2\)
11. \(9a^{7}-49a^{5}=a^{5}(9a^{2}-49)=a^{5}(3a+7)(3a-7)\)
12. \(-50x^{9}+40x^{7}-8x^{5}=-2x^{5}(25x^{4}-20x^2+4)=-2x^{5}(5x^2-2)^2\)