Ontbinden in factoren (2)

Hoofdmenu Eentje per keer  🖨

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

1. \(125s^{5}+100s^{4}+20s^{3}\)
2. \(-384p^{7}-96p^{6}-6p^{5}\)
3. \(-108y^{19}+75y^{5}\)
4. \(9x^{9}-30x^{6}+25x^{3}\)
5. \(180a^{9}-5a^{3}\)
6. \(25s^{6}-36s^{4}\)
7. \(-36q^{12}+60q^{7}-25q^{2}\)
8. \(-64q^{6}-16q^{4}s-q^{2}s^2\)
9. \(-2y^{7}-12y^{6}-18y^{5}\)
10. \(16b^{7}-56b^{5}y+49b^{3}y^2\)
11. \(5b^{7}-5b^{5}\)
12. \(20s^{4}-45s^{2}\)

---

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

Verbetersleutel

1. \(125s^{5}+100s^{4}+20s^{3}=5s^{3}(25s^{2}+20s+4)=5s^{3}(5s+2)^2\)
2. \(-384p^{7}-96p^{6}-6p^{5}=-6p^{5}(64p^{2}+16p+1)=-6p^{5}(8p+1)^2\)
3. \(-108y^{19}+75y^{5}=-3y^{5}(36y^{14}-25)=-3y^{5}(6y^7+5)(6y^7-5)\)
4. \(9x^{9}-30x^{6}+25x^{3}=x^{3}(9x^{6}-30x^3+25)=x^{3}(3x^3-5)^2\)
5. \(180a^{9}-5a^{3}=5a^{3}(36a^{6}-1)=5a^{3}(6a^3+1)(6a^3-1)\)
6. \(25s^{6}-36s^{4}=s^{4}(25s^{2}-36)=s^{4}(5s+6)(5s-6)\)
7. \(-36q^{12}+60q^{7}-25q^{2}=-q^{2}(36q^{10}-60q^5+25)=-q^{2}(6q^5-5)^2\)
8. \(-64q^{6}-16q^{4}s-q^{2}s^2=-q^{2}(64q^{4}+16q^2s+s^2)=-q^{2}(8q^2+s)^2\)
9. \(-2y^{7}-12y^{6}-18y^{5}=-2y^{5}(y^2+6y+9)=-2y^{5}(y+3)^2\)
10. \(16b^{7}-56b^{5}y+49b^{3}y^2=b^{3}(16b^{4}-56b^2y+49y^2)=b^{3}(4b^2-7y)^2\)
11. \(5b^{7}-5b^{5}=5b^{5}(b^2-1)=5b^{5}(b+1)(b-1)\)
12. \(20s^{4}-45s^{2}=5s^{2}(4s^{2}-9)=5s^{2}(2s+3)(2s-3)\)