Ontbinden in factoren (2)

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

1. \(3b^{6}-30b^{5}+75b^{4}\)
2. \(54s^{19}-294s^{3}\)
3. \(72q^{7}-50q^{5}\)
4. \(-6x^{6}+216x^{4}\)
5. \(-98a^{10}-112a^{7}-32a^{4}\)
6. \(-25q^{6}-20q^{5}-4q^{4}\)
7. \(-27s^{5}+12s^{3}\)
8. \(48a^{5}-3a^{3}\)
9. \(-80x^{6}+45x^{4}\)
10. \(20p^{9}+20p^{6}y+5p^{3}y^2\)
11. \(-36y^{16}+25y^{2}\)
12. \(5x^{5}-80x^{4}+320x^{3}\)

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

Verbetersleutel

1. \(3b^{6}-30b^{5}+75b^{4}=3b^{4}(b^2-10b+25)=3b^{4}(b-5)^2\)
2. \(54s^{19}-294s^{3}=6s^{3}(9s^{16}-49)=6s^{3}(3s^8+7)(3s^8-7)\)
3. \(72q^{7}-50q^{5}=2q^{5}(36q^{2}-25)=2q^{5}(6q+5)(6q-5)\)
4. \(-6x^{6}+216x^{4}=-6x^{4}(x^2-36)=-6x^{4}(x+6)(x-6)\)
5. \(-98a^{10}-112a^{7}-32a^{4}=-2a^{4}(49a^{6}+56a^3+16)=-2a^{4}(7a^3+4)^2\)
6. \(-25q^{6}-20q^{5}-4q^{4}=-q^{4}(25q^{2}+20q+4)=-q^{4}(5q+2)^2\)
7. \(-27s^{5}+12s^{3}=-3s^{3}(9s^{2}-4)=-3s^{3}(3s+2)(3s-2)\)
8. \(48a^{5}-3a^{3}=3a^{3}(16a^{2}-1)=3a^{3}(4a+1)(4a-1)\)
9. \(-80x^{6}+45x^{4}=-5x^{4}(16x^{2}-9)=-5x^{4}(4x+3)(4x-3)\)
10. \(20p^{9}+20p^{6}y+5p^{3}y^2=5p^{3}(4p^{6}+4p^3y+y^2)=5p^{3}(2p^3+y)^2\)
11. \(-36y^{16}+25y^{2}=-y^{2}(36y^{14}-25)=-y^{2}(6y^7+5)(6y^7-5)\)
12. \(5x^{5}-80x^{4}+320x^{3}=5x^{3}(x^2-16x+64)=5x^{3}(x-8)^2\)