Ontbinden in factoren (2)

Hoofdmenu Eentje per keer  🖨

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

1. \(4q^{11}+4q^{8}y+q^{5}y^2\)
2. \(-32a^{12}+48a^{8}p-18a^{4}p^2\)
3. \(150b^{21}-216b^{5}\)
4. \(-75x^{6}+120x^{5}-48x^{4}\)
5. \(-54p^{7}+96p^{5}\)
6. \(-125a^{7}+80a^{5}\)
7. \(36a^{8}+12a^{5}x+a^{2}x^2\)
8. \(-6x^{5}+54x^{3}\)
9. \(-2p^{6}+72p^{4}\)
10. \(48x^{4}+72x^{3}+27x^{2}\)
11. \(36b^{13}+60b^{8}q+25b^{3}q^2\)
12. \(a^{6}-a^{4}\)

---

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

Verbetersleutel

1. \(4q^{11}+4q^{8}y+q^{5}y^2=q^{5}(4q^{6}+4q^3y+y^2)=q^{5}(2q^3+y)^2\)
2. \(-32a^{12}+48a^{8}p-18a^{4}p^2=-2a^{4}(16a^{8}-24a^4p+9p^2)=-2a^{4}(4a^4-3p)^2\)
3. \(150b^{21}-216b^{5}=6b^{5}(25b^{16}-36)=6b^{5}(5b^8+6)(5b^8-6)\)
4. \(-75x^{6}+120x^{5}-48x^{4}=-3x^{4}(25x^{2}-40x+16)=-3x^{4}(5x-4)^2\)
5. \(-54p^{7}+96p^{5}=-6p^{5}(9p^{2}-16)=-6p^{5}(3p+4)(3p-4)\)
6. \(-125a^{7}+80a^{5}=-5a^{5}(25a^{2}-16)=-5a^{5}(5a+4)(5a-4)\)
7. \(36a^{8}+12a^{5}x+a^{2}x^2=a^{2}(36a^{6}+12a^3x+x^2)=a^{2}(6a^3+x)^2\)
8. \(-6x^{5}+54x^{3}=-6x^{3}(x^2-9)=-6x^{3}(x+3)(x-3)\)
9. \(-2p^{6}+72p^{4}=-2p^{4}(p^2-36)=-2p^{4}(p+6)(p-6)\)
10. \(48x^{4}+72x^{3}+27x^{2}=3x^{2}(16x^{2}+24x+9)=3x^{2}(4x+3)^2\)
11. \(36b^{13}+60b^{8}q+25b^{3}q^2=b^{3}(36b^{10}+60b^5q+25q^2)=b^{3}(6b^5+5q)^2\)
12. \(a^{6}-a^{4}=a^{4}(a^2-1)=a^{4}(a-1)(a+1)\)