Ontbinden in factoren (2)

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

1. \(-48x^{6}+72x^{4}-27x^{2}\)
2. \(-98x^{13}-28x^{8}y-2x^{3}y^2\)
3. \(45y^{5}-5y^{3}\)
4. \(180y^{12}-300y^{7}+125y^{2}\)
5. \(2y^{5}-2y^{3}\)
6. \(2s^{6}-4s^{5}+2s^{4}\)
7. \(-75y^{5}-120y^{4}-48y^{3}\)
8. \(-128s^{4}+224s^{3}-98s^{2}\)
9. \(-2b^{7}+128b^{5}\)
10. \(18y^{4}-2y^{2}\)
11. \(72x^{13}+120x^{9}+50x^{5}\)
12. \(54s^{5}-294s^{3}\)

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

Verbetersleutel

1. \(-48x^{6}+72x^{4}-27x^{2}=-3x^{2}(16x^{4}-24x^2+9)=-3x^{2}(4x^2-3)^2\)
2. \(-98x^{13}-28x^{8}y-2x^{3}y^2=-2x^{3}(49x^{10}+14x^5y+y^2)=-2x^{3}(7x^5+y)^2\)
3. \(45y^{5}-5y^{3}=5y^{3}(9y^{2}-1)=5y^{3}(3y+1)(3y-1)\)
4. \(180y^{12}-300y^{7}+125y^{2}=5y^{2}(36y^{10}-60y^5+25)=5y^{2}(6y^5-5)^2\)
5. \(2y^{5}-2y^{3}=2y^{3}(y^2-1)=2y^{3}(y+1)(y-1)\)
6. \(2s^{6}-4s^{5}+2s^{4}=2s^{4}(s^2-2s+1)=2s^{4}(s-1)^2\)
7. \(-75y^{5}-120y^{4}-48y^{3}=-3y^{3}(25y^{2}+40y+16)=-3y^{3}(5y+4)^2\)
8. \(-128s^{4}+224s^{3}-98s^{2}=-2s^{2}(64s^{2}-112s+49)=-2s^{2}(8s-7)^2\)
9. \(-2b^{7}+128b^{5}=-2b^{5}(b^2-64)=-2b^{5}(b-8)(b+8)\)
10. \(18y^{4}-2y^{2}=2y^{2}(9y^{2}-1)=2y^{2}(3y+1)(3y-1)\)
11. \(72x^{13}+120x^{9}+50x^{5}=2x^{5}(36x^{8}+60x^4+25)=2x^{5}(6x^4+5)^2\)
12. \(54s^{5}-294s^{3}=6s^{3}(9s^{2}-49)=6s^{3}(3s+7)(3s-7)\)