Ontbinden in factoren (2)

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

1. \(-320s^{11}+400s^{8}x-125s^{5}x^2\)
2. \(150b^{9}-6b^{3}\)
3. \(-80q^{6}-200q^{4}-125q^{2}\)
4. \(-20b^{9}-20b^{6}-5b^{3}\)
5. \(18b^{20}-8b^{4}\)
6. \(-36s^{7}+s^{3}\)
7. \(8y^{5}+8y^{4}+2y^{3}\)
8. \(-27a^{13}+90a^{9}-75a^{5}\)
9. \(-24y^{5}-24y^{4}-6y^{3}\)
10. \(-72s^{6}+50s^{2}\)
11. \(96p^{7}-6p^{5}\)
12. \(-75p^{13}+210p^{9}x-147p^{5}x^2\)

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

Verbetersleutel

1. \(-320s^{11}+400s^{8}x-125s^{5}x^2=-5s^{5}(64s^{6}-80s^3x+25x^2)=-5s^{5}(8s^3-5x)^2\)
2. \(150b^{9}-6b^{3}=6b^{3}(25b^{6}-1)=6b^{3}(5b^3+1)(5b^3-1)\)
3. \(-80q^{6}-200q^{4}-125q^{2}=-5q^{2}(16q^{4}+40q^2+25)=-5q^{2}(4q^2+5)^2\)
4. \(-20b^{9}-20b^{6}-5b^{3}=-5b^{3}(4b^{6}+4b^3+1)=-5b^{3}(2b^3+1)^2\)
5. \(18b^{20}-8b^{4}=2b^{4}(9b^{16}-4)=2b^{4}(3b^8+2)(3b^8-2)\)
6. \(-36s^{7}+s^{3}=-s^{3}(36s^{4}-1)=-s^{3}(6s^2+1)(6s^2-1)\)
7. \(8y^{5}+8y^{4}+2y^{3}=2y^{3}(4y^{2}+4y+1)=2y^{3}(2y+1)^2\)
8. \(-27a^{13}+90a^{9}-75a^{5}=-3a^{5}(9a^{8}-30a^4+25)=-3a^{5}(3a^4-5)^2\)
9. \(-24y^{5}-24y^{4}-6y^{3}=-6y^{3}(4y^{2}+4y+1)=-6y^{3}(2y+1)^2\)
10. \(-72s^{6}+50s^{2}=-2s^{2}(36s^{4}-25)=-2s^{2}(6s^2+5)(6s^2-5)\)
11. \(96p^{7}-6p^{5}=6p^{5}(16p^{2}-1)=6p^{5}(4p+1)(4p-1)\)
12. \(-75p^{13}+210p^{9}x-147p^{5}x^2=-3p^{5}(25p^{8}-70p^4x+49x^2)=-3p^{5}(5p^4-7x)^2\)