Ontbinden in factoren (2)

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

1. \(245y^{7}-210y^{6}+45y^{5}\)
2. \(20s^{12}-45s^{4}\)
3. \(-75p^{9}+120p^{7}-48p^{5}\)
4. \(6a^{5}-384a^{3}\)
5. \(5b^{7}-125b^{5}\)
6. \(2a^{5}-2a^{3}\)
7. \(-180x^{12}-300x^{7}-125x^{2}\)
8. \(25a^{11}-70a^{7}x+49a^{3}x^2\)
9. \(-27s^{6}-72s^{5}-48s^{4}\)
10. \(x^{6}-x^{4}\)
11. \(64y^{7}+16y^{6}+y^{5}\)
12. \(4q^{7}-25q^{3}\)

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

Verbetersleutel

1. \(245y^{7}-210y^{6}+45y^{5}=5y^{5}(49y^{2}-42y+9)=5y^{5}(7y-3)^2\)
2. \(20s^{12}-45s^{4}=5s^{4}(4s^{8}-9)=5s^{4}(2s^4+3)(2s^4-3)\)
3. \(-75p^{9}+120p^{7}-48p^{5}=-3p^{5}(25p^{4}-40p^2+16)=-3p^{5}(5p^2-4)^2\)
4. \(6a^{5}-384a^{3}=6a^{3}(a^2-64)=6a^{3}(a+8)(a-8)\)
5. \(5b^{7}-125b^{5}=5b^{5}(b^2-25)=5b^{5}(b-5)(b+5)\)
6. \(2a^{5}-2a^{3}=2a^{3}(a^2-1)=2a^{3}(a-1)(a+1)\)
7. \(-180x^{12}-300x^{7}-125x^{2}=-5x^{2}(36x^{10}+60x^5+25)=-5x^{2}(6x^5+5)^2\)
8. \(25a^{11}-70a^{7}x+49a^{3}x^2=a^{3}(25a^{8}-70a^4x+49x^2)=a^{3}(5a^4-7x)^2\)
9. \(-27s^{6}-72s^{5}-48s^{4}=-3s^{4}(9s^{2}+24s+16)=-3s^{4}(3s+4)^2\)
10. \(x^{6}-x^{4}=x^{4}(x^2-1)=x^{4}(x-1)(x+1)\)
11. \(64y^{7}+16y^{6}+y^{5}=y^{5}(64y^{2}+16y+1)=y^{5}(8y+1)^2\)
12. \(4q^{7}-25q^{3}=q^{3}(4q^{4}-25)=q^{3}(2q^2+5)(2q^2-5)\)