Ontbinden in factoren (2)

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

1. \(-75b^{12}-60b^{8}-12b^{4}\)
2. \(-9s^{11}+25s^{3}\)
3. \(96y^{19}-6y^{3}\)
4. \(-48b^{10}-120b^{7}x-75b^{4}x^2\)
5. \(-384p^{13}+672p^{8}x-294p^{3}x^2\)
6. \(108b^{11}+36b^{8}x+3b^{5}x^2\)
7. \(3q^{4}-3q^{2}\)
8. \(-4q^{13}-4q^{9}y-q^{5}y^2\)
9. \(-80q^{12}-40q^{8}x-5q^{4}x^2\)
10. \(-45p^{10}+60p^{7}y-20p^{4}y^2\)
11. \(5q^{7}-80q^{5}\)
12. \(a^{4}-8a^{3}+16a^{2}\)

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

Verbetersleutel

1. \(-75b^{12}-60b^{8}-12b^{4}=-3b^{4}(25b^{8}+20b^4+4)=-3b^{4}(5b^4+2)^2\)
2. \(-9s^{11}+25s^{3}=-s^{3}(9s^{8}-25)=-s^{3}(3s^4+5)(3s^4-5)\)
3. \(96y^{19}-6y^{3}=6y^{3}(16y^{16}-1)=6y^{3}(4y^8+1)(4y^8-1)\)
4. \(-48b^{10}-120b^{7}x-75b^{4}x^2=-3b^{4}(16b^{6}+40b^3x+25x^2)=-3b^{4}(4b^3+5x)^2\)
5. \(-384p^{13}+672p^{8}x-294p^{3}x^2=-6p^{3}(64p^{10}-112p^5x+49x^2)=-6p^{3}(8p^5-7x)^2\)
6. \(108b^{11}+36b^{8}x+3b^{5}x^2=3b^{5}(36b^{6}+12b^3x+x^2)=3b^{5}(6b^3+x)^2\)
7. \(3q^{4}-3q^{2}=3q^{2}(q^2-1)=3q^{2}(q-1)(q+1)\)
8. \(-4q^{13}-4q^{9}y-q^{5}y^2=-q^{5}(4q^{8}+4q^4y+y^2)=-q^{5}(2q^4+y)^2\)
9. \(-80q^{12}-40q^{8}x-5q^{4}x^2=-5q^{4}(16q^{8}+8q^4x+x^2)=-5q^{4}(4q^4+x)^2\)
10. \(-45p^{10}+60p^{7}y-20p^{4}y^2=-5p^{4}(9p^{6}-12p^3y+4y^2)=-5p^{4}(3p^3-2y)^2\)
11. \(5q^{7}-80q^{5}=5q^{5}(q^2-16)=5q^{5}(q-4)(q+4)\)
12. \(a^{4}-8a^{3}+16a^{2}=a^{2}(a^2-8a+16)=a^{2}(a-4)^2\)