Ontbinden in factoren (2)

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

1. \(-25s^{5}+49s^{3}\)
2. \(49y^{5}+112y^{4}+64y^{3}\)
3. \(96s^{13}-336s^{9}+294s^{5}\)
4. \(-3q^{4}+48q^{3}-192q^{2}\)
5. \(-150q^{7}+6q^{5}\)
6. \(9q^{13}-30q^{9}+25q^{5}\)
7. \(-64q^{6}-16q^{4}-q^{2}\)
8. \(8q^{12}+8q^{7}+2q^{2}\)
9. \(72a^{5}+24a^{4}+2a^{3}\)
10. \(-50s^{11}+40s^{7}-8s^{3}\)
11. \(50y^{6}-72y^{4}\)
12. \(32b^{15}-48b^{10}y+18b^{5}y^2\)

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

Verbetersleutel

1. \(-25s^{5}+49s^{3}=-s^{3}(25s^{2}-49)=-s^{3}(5s+7)(5s-7)\)
2. \(49y^{5}+112y^{4}+64y^{3}=y^{3}(49y^{2}+112y+64)=y^{3}(7y+8)^2\)
3. \(96s^{13}-336s^{9}+294s^{5}=6s^{5}(16s^{8}-56s^4+49)=6s^{5}(4s^4-7)^2\)
4. \(-3q^{4}+48q^{3}-192q^{2}=-3q^{2}(q^2-16q+64)=-3q^{2}(q-8)^2\)
5. \(-150q^{7}+6q^{5}=-6q^{5}(25q^{2}-1)=-6q^{5}(5q+1)(5q-1)\)
6. \(9q^{13}-30q^{9}+25q^{5}=q^{5}(9q^{8}-30q^4+25)=q^{5}(3q^4-5)^2\)
7. \(-64q^{6}-16q^{4}-q^{2}=-q^{2}(64q^{4}+16q^2+1)=-q^{2}(8q^2+1)^2\)
8. \(8q^{12}+8q^{7}+2q^{2}=2q^{2}(4q^{10}+4q^5+1)=2q^{2}(2q^5+1)^2\)
9. \(72a^{5}+24a^{4}+2a^{3}=2a^{3}(36a^{2}+12a+1)=2a^{3}(6a+1)^2\)
10. \(-50s^{11}+40s^{7}-8s^{3}=-2s^{3}(25s^{8}-20s^4+4)=-2s^{3}(5s^4-2)^2\)
11. \(50y^{6}-72y^{4}=2y^{4}(25y^{2}-36)=2y^{4}(5y+6)(5y-6)\)
12. \(32b^{15}-48b^{10}y+18b^{5}y^2=2b^{5}(16b^{10}-24b^5y+9y^2)=2b^{5}(4b^5-3y)^2\)