Ontbinden in factoren (2)

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

1. \(-50b^{12}+8b^{2}\)
2. \(75y^{5}+180y^{4}+108y^{3}\)
3. \(80a^{13}-120a^{8}p+45a^{3}p^2\)
4. \(-96x^{12}+294x^{2}\)
5. \(96y^{17}-150y^{3}\)
6. \(108s^{7}-180s^{6}+75s^{5}\)
7. \(-25y^{11}+49y^{3}\)
8. \(-27q^{21}+147q^{5}\)
9. \(75p^{14}-120p^{9}x+48p^{4}x^2\)
10. \(-2p^{6}+8p^{4}\)
11. \(-2q^{7}+128q^{5}\)
12. \(8b^{13}+8b^{9}y+2b^{5}y^2\)

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

Verbetersleutel

1. \(-50b^{12}+8b^{2}=-2b^{2}(25b^{10}-4)=-2b^{2}(5b^5+2)(5b^5-2)\)
2. \(75y^{5}+180y^{4}+108y^{3}=3y^{3}(25y^{2}+60y+36)=3y^{3}(5y+6)^2\)
3. \(80a^{13}-120a^{8}p+45a^{3}p^2=5a^{3}(16a^{10}-24a^5p+9p^2)=5a^{3}(4a^5-3p)^2\)
4. \(-96x^{12}+294x^{2}=-6x^{2}(16x^{10}-49)=-6x^{2}(4x^5+7)(4x^5-7)\)
5. \(96y^{17}-150y^{3}=6y^{3}(16y^{14}-25)=6y^{3}(4y^7+5)(4y^7-5)\)
6. \(108s^{7}-180s^{6}+75s^{5}=3s^{5}(36s^{2}-60s+25)=3s^{5}(6s-5)^2\)
7. \(-25y^{11}+49y^{3}=-y^{3}(25y^{8}-49)=-y^{3}(5y^4+7)(5y^4-7)\)
8. \(-27q^{21}+147q^{5}=-3q^{5}(9q^{16}-49)=-3q^{5}(3q^8+7)(3q^8-7)\)
9. \(75p^{14}-120p^{9}x+48p^{4}x^2=3p^{4}(25p^{10}-40p^5x+16x^2)=3p^{4}(5p^5-4x)^2\)
10. \(-2p^{6}+8p^{4}=-2p^{4}(p^2-4)=-2p^{4}(p-2)(p+2)\)
11. \(-2q^{7}+128q^{5}=-2q^{5}(q^2-64)=-2q^{5}(q-8)(q+8)\)
12. \(8b^{13}+8b^{9}y+2b^{5}y^2=2b^{5}(4b^{8}+4b^4y+y^2)=2b^{5}(2b^4+y)^2\)