Ontbinden in factoren (2)

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

1. \(80x^{4}-45x^{2}\)
2. \(12q^{11}+36q^{8}+27q^{5}\)
3. \(180q^{10}+420q^{7}s+245q^{4}s^2\)
4. \(216s^{11}-294s^{5}\)
5. \(2p^{5}-32p^{3}\)
6. \(24a^{11}-294a^{3}\)
7. \(-96q^{4}+294q^{2}\)
8. \(-72b^{7}+120b^{5}s-50b^{3}s^2\)
9. \(-y^{6}+64y^{4}\)
10. \(-50s^{6}-20s^{4}-2s^{2}\)
11. \(-5s^{6}-10s^{5}-5s^{4}\)
12. \(108y^{4}-180y^{3}+75y^{2}\)

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

Verbetersleutel

1. \(80x^{4}-45x^{2}=5x^{2}(16x^{2}-9)=5x^{2}(4x+3)(4x-3)\)
2. \(12q^{11}+36q^{8}+27q^{5}=3q^{5}(4q^{6}+12q^3+9)=3q^{5}(2q^3+3)^2\)
3. \(180q^{10}+420q^{7}s+245q^{4}s^2=5q^{4}(36q^{6}+84q^3s+49s^2)=5q^{4}(6q^3+7s)^2\)
4. \(216s^{11}-294s^{5}=6s^{5}(36s^{6}-49)=6s^{5}(6s^3+7)(6s^3-7)\)
5. \(2p^{5}-32p^{3}=2p^{3}(p^2-16)=2p^{3}(p+4)(p-4)\)
6. \(24a^{11}-294a^{3}=6a^{3}(4a^{8}-49)=6a^{3}(2a^4+7)(2a^4-7)\)
7. \(-96q^{4}+294q^{2}=-6q^{2}(16q^{2}-49)=-6q^{2}(4q+7)(4q-7)\)
8. \(-72b^{7}+120b^{5}s-50b^{3}s^2=-2b^{3}(36b^{4}-60b^2s+25s^2)=-2b^{3}(6b^2-5s)^2\)
9. \(-y^{6}+64y^{4}=-y^{4}(y^2-64)=-y^{4}(y+8)(y-8)\)
10. \(-50s^{6}-20s^{4}-2s^{2}=-2s^{2}(25s^{4}+10s^2+1)=-2s^{2}(5s^2+1)^2\)
11. \(-5s^{6}-10s^{5}-5s^{4}=-5s^{4}(s^2+2s+1)=-5s^{4}(s+1)^2\)
12. \(108y^{4}-180y^{3}+75y^{2}=3y^{2}(36y^{2}-60y+25)=3y^{2}(6y-5)^2\)