Ontbinden in factoren (2)

Hoofdmenu Eentje per keer  🖨

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

1. \(50s^{5}-2s^{3}\)
2. \(-20y^{5}-140y^{4}-245y^{3}\)
3. \(2p^{4}+4p^{3}+2p^{2}\)
4. \(-32q^{7}+50q^{5}\)
5. \(6q^{6}-24q^{4}\)
6. \(80p^{10}-120p^{7}y+45p^{4}y^2\)
7. \(3q^{4}-75q^{2}\)
8. \(-108b^{8}-180b^{6}x-75b^{4}x^2\)
9. \(2s^{5}+32s^{4}+128s^{3}\)
10. \(125s^{9}+200s^{6}y+80s^{3}y^2\)
11. \(-32y^{4}+18y^{2}\)
12. \(2a^{6}-18a^{4}\)

---

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

Verbetersleutel

1. \(50s^{5}-2s^{3}=2s^{3}(25s^{2}-1)=2s^{3}(5s+1)(5s-1)\)
2. \(-20y^{5}-140y^{4}-245y^{3}=-5y^{3}(4y^{2}+28y+49)=-5y^{3}(2y+7)^2\)
3. \(2p^{4}+4p^{3}+2p^{2}=2p^{2}(p^2+2p+1)=2p^{2}(p+1)^2\)
4. \(-32q^{7}+50q^{5}=-2q^{5}(16q^{2}-25)=-2q^{5}(4q+5)(4q-5)\)
5. \(6q^{6}-24q^{4}=6q^{4}(q^2-4)=6q^{4}(q-2)(q+2)\)
6. \(80p^{10}-120p^{7}y+45p^{4}y^2=5p^{4}(16p^{6}-24p^3y+9y^2)=5p^{4}(4p^3-3y)^2\)
7. \(3q^{4}-75q^{2}=3q^{2}(q^2-25)=3q^{2}(q+5)(q-5)\)
8. \(-108b^{8}-180b^{6}x-75b^{4}x^2=-3b^{4}(36b^{4}+60b^2x+25x^2)=-3b^{4}(6b^2+5x)^2\)
9. \(2s^{5}+32s^{4}+128s^{3}=2s^{3}(s^2+16s+64)=2s^{3}(s+8)^2\)
10. \(125s^{9}+200s^{6}y+80s^{3}y^2=5s^{3}(25s^{6}+40s^3y+16y^2)=5s^{3}(5s^3+4y)^2\)
11. \(-32y^{4}+18y^{2}=-2y^{2}(16y^{2}-9)=-2y^{2}(4y+3)(4y-3)\)
12. \(2a^{6}-18a^{4}=2a^{4}(a^2-9)=2a^{4}(a-3)(a+3)\)