Ontbinden in factoren (2)

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

1. \(320x^{5}-400x^{4}+125x^{3}\)
2. \(-48x^{14}-72x^{9}-27x^{4}\)
3. \(50x^{7}-18x^{5}\)
4. \(-2x^{5}+98x^{3}\)
5. \(72a^{9}+24a^{6}b+2a^{3}b^2\)
6. \(3x^{5}-192x^{3}\)
7. \(-96a^{12}+294a^{2}\)
8. \(49a^{15}-42a^{10}s+9a^{5}s^2\)
9. \(3x^{7}+12x^{6}+12x^{5}\)
10. \(-20p^{4}+45p^{2}\)
11. \(27y^{16}-48y^{2}\)
12. \(-25b^{6}-10b^{4}-b^{2}\)

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

Verbetersleutel

1. \(320x^{5}-400x^{4}+125x^{3}=5x^{3}(64x^{2}-80x+25)=5x^{3}(8x-5)^2\)
2. \(-48x^{14}-72x^{9}-27x^{4}=-3x^{4}(16x^{10}+24x^5+9)=-3x^{4}(4x^5+3)^2\)
3. \(50x^{7}-18x^{5}=2x^{5}(25x^{2}-9)=2x^{5}(5x+3)(5x-3)\)
4. \(-2x^{5}+98x^{3}=-2x^{3}(x^2-49)=-2x^{3}(x+7)(x-7)\)
5. \(72a^{9}+24a^{6}b+2a^{3}b^2=2a^{3}(36a^{6}+12a^3b+b^2)=2a^{3}(6a^3+b)^2\)
6. \(3x^{5}-192x^{3}=3x^{3}(x^2-64)=3x^{3}(x+8)(x-8)\)
7. \(-96a^{12}+294a^{2}=-6a^{2}(16a^{10}-49)=-6a^{2}(4a^5+7)(4a^5-7)\)
8. \(49a^{15}-42a^{10}s+9a^{5}s^2=a^{5}(49a^{10}-42a^5s+9s^2)=a^{5}(7a^5-3s)^2\)
9. \(3x^{7}+12x^{6}+12x^{5}=3x^{5}(x^2+4x+4)=3x^{5}(x+2)^2\)
10. \(-20p^{4}+45p^{2}=-5p^{2}(4p^{2}-9)=-5p^{2}(2p+3)(2p-3)\)
11. \(27y^{16}-48y^{2}=3y^{2}(9y^{14}-16)=3y^{2}(3y^7+4)(3y^7-4)\)
12. \(-25b^{6}-10b^{4}-b^{2}=-b^{2}(25b^{4}+10b^2+1)=-b^{2}(5b^2+1)^2\)