Ontbinden in factoren (2)

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

1. \(49b^{9}-42b^{7}q+9b^{5}q^2\)
2. \(-80x^{5}+245x^{3}\)
3. \(-2s^{5}-12s^{4}-18s^{3}\)
4. \(-16a^{4}+9a^{2}\)
5. \(12p^{11}-147p^{3}\)
6. \(3b^{6}-27b^{4}\)
7. \(-9p^{8}+p^{4}\)
8. \(-50x^{7}+32x^{5}\)
9. \(-4x^{6}-4x^{5}-x^{4}\)
10. \(-16s^{9}+56s^{7}x-49s^{5}x^2\)
11. \(125a^{15}-350a^{10}p+245a^{5}p^2\)
12. \(25x^{6}-x^{4}\)

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

Verbetersleutel

1. \(49b^{9}-42b^{7}q+9b^{5}q^2=b^{5}(49b^{4}-42b^2q+9q^2)=b^{5}(7b^2-3q)^2\)
2. \(-80x^{5}+245x^{3}=-5x^{3}(16x^{2}-49)=-5x^{3}(4x+7)(4x-7)\)
3. \(-2s^{5}-12s^{4}-18s^{3}=-2s^{3}(s^2+6s+9)=-2s^{3}(s+3)^2\)
4. \(-16a^{4}+9a^{2}=-a^{2}(16a^{2}-9)=-a^{2}(4a+3)(4a-3)\)
5. \(12p^{11}-147p^{3}=3p^{3}(4p^{8}-49)=3p^{3}(2p^4+7)(2p^4-7)\)
6. \(3b^{6}-27b^{4}=3b^{4}(b^2-9)=3b^{4}(b-3)(b+3)\)
7. \(-9p^{8}+p^{4}=-p^{4}(9p^{4}-1)=-p^{4}(3p^2+1)(3p^2-1)\)
8. \(-50x^{7}+32x^{5}=-2x^{5}(25x^{2}-16)=-2x^{5}(5x+4)(5x-4)\)
9. \(-4x^{6}-4x^{5}-x^{4}=-x^{4}(4x^{2}+4x+1)=-x^{4}(2x+1)^2\)
10. \(-16s^{9}+56s^{7}x-49s^{5}x^2=-s^{5}(16s^{4}-56s^2x+49x^2)=-s^{5}(4s^2-7x)^2\)
11. \(125a^{15}-350a^{10}p+245a^{5}p^2=5a^{5}(25a^{10}-70a^5p+49p^2)=5a^{5}(5a^5-7p)^2\)
12. \(25x^{6}-x^{4}=x^{4}(25x^{2}-1)=x^{4}(5x+1)(5x-1)\)