Ontbinden in factoren (2)

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

1. \(-32q^{4}+18q^{2}\)
2. \(18s^{9}-8s^{5}\)
3. \(-2y^{6}+50y^{4}\)
4. \(5a^{7}-70a^{6}+245a^{5}\)
5. \(-4b^{10}-20b^{7}y-25b^{4}y^2\)
6. \(-3q^{5}+3q^{3}\)
7. \(20s^{11}+20s^{7}y+5s^{3}y^2\)
8. \(192y^{7}+48y^{6}+3y^{5}\)
9. \(-6y^{6}+96y^{4}\)
10. \(-54y^{4}+6y^{2}\)
11. \(6x^{5}-384x^{3}\)
12. \(q^{4}-16q^{2}\)

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

Verbetersleutel

1. \(-32q^{4}+18q^{2}=-2q^{2}(16q^{2}-9)=-2q^{2}(4q+3)(4q-3)\)
2. \(18s^{9}-8s^{5}=2s^{5}(9s^{4}-4)=2s^{5}(3s^2+2)(3s^2-2)\)
3. \(-2y^{6}+50y^{4}=-2y^{4}(y^2-25)=-2y^{4}(y-5)(y+5)\)
4. \(5a^{7}-70a^{6}+245a^{5}=5a^{5}(a^2-14a+49)=5a^{5}(a-7)^2\)
5. \(-4b^{10}-20b^{7}y-25b^{4}y^2=-b^{4}(4b^{6}+20b^3y+25y^2)=-b^{4}(2b^3+5y)^2\)
6. \(-3q^{5}+3q^{3}=-3q^{3}(q^2-1)=-3q^{3}(q-1)(q+1)\)
7. \(20s^{11}+20s^{7}y+5s^{3}y^2=5s^{3}(4s^{8}+4s^4y+y^2)=5s^{3}(2s^4+y)^2\)
8. \(192y^{7}+48y^{6}+3y^{5}=3y^{5}(64y^{2}+16y+1)=3y^{5}(8y+1)^2\)
9. \(-6y^{6}+96y^{4}=-6y^{4}(y^2-16)=-6y^{4}(y-4)(y+4)\)
10. \(-54y^{4}+6y^{2}=-6y^{2}(9y^{2}-1)=-6y^{2}(3y+1)(3y-1)\)
11. \(6x^{5}-384x^{3}=6x^{3}(x^2-64)=6x^{3}(x+8)(x-8)\)
12. \(q^{4}-16q^{2}=q^{2}(q^2-16)=q^{2}(q+4)(q-4)\)