Ontbinden in factoren (2)

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

1. \(-3b^{5}+108b^{3}\)
2. \(-150s^{12}+240s^{7}-96s^{2}\)
3. \(108b^{12}-180b^{8}+75b^{4}\)
4. \(384p^{7}+96p^{6}+6p^{5}\)
5. \(96q^{12}+240q^{8}+150q^{4}\)
6. \(-2q^{6}+28q^{5}-98q^{4}\)
7. \(-80p^{13}+280p^{8}-245p^{3}\)
8. \(-25b^{7}-30b^{6}-9b^{5}\)
9. \(49s^{9}+70s^{7}y+25s^{5}y^2\)
10. \(6p^{7}-96p^{5}\)
11. \(-20b^{9}-60b^{6}-45b^{3}\)
12. \(-75q^{18}+3q^{4}\)

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

Verbetersleutel

1. \(-3b^{5}+108b^{3}=-3b^{3}(b^2-36)=-3b^{3}(b+6)(b-6)\)
2. \(-150s^{12}+240s^{7}-96s^{2}=-6s^{2}(25s^{10}-40s^5+16)=-6s^{2}(5s^5-4)^2\)
3. \(108b^{12}-180b^{8}+75b^{4}=3b^{4}(36b^{8}-60b^4+25)=3b^{4}(6b^4-5)^2\)
4. \(384p^{7}+96p^{6}+6p^{5}=6p^{5}(64p^{2}+16p+1)=6p^{5}(8p+1)^2\)
5. \(96q^{12}+240q^{8}+150q^{4}=6q^{4}(16q^{8}+40q^4+25)=6q^{4}(4q^4+5)^2\)
6. \(-2q^{6}+28q^{5}-98q^{4}=-2q^{4}(q^2-14q+49)=-2q^{4}(q-7)^2\)
7. \(-80p^{13}+280p^{8}-245p^{3}=-5p^{3}(16p^{10}-56p^5+49)=-5p^{3}(4p^5-7)^2\)
8. \(-25b^{7}-30b^{6}-9b^{5}=-b^{5}(25b^{2}+30b+9)=-b^{5}(5b+3)^2\)
9. \(49s^{9}+70s^{7}y+25s^{5}y^2=s^{5}(49s^{4}+70s^2y+25y^2)=s^{5}(7s^2+5y)^2\)
10. \(6p^{7}-96p^{5}=6p^{5}(p^2-16)=6p^{5}(p-4)(p+4)\)
11. \(-20b^{9}-60b^{6}-45b^{3}=-5b^{3}(4b^{6}+12b^3+9)=-5b^{3}(2b^3+3)^2\)
12. \(-75q^{18}+3q^{4}=-3q^{4}(25q^{14}-1)=-3q^{4}(5q^7+1)(5q^7-1)\)