Ontbinden in factoren (2)

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

1. \(9x^{7}-49x^{5}\)
2. \(320p^{10}-560p^{6}x+245p^{2}x^2\)
3. \(-150q^{10}+54q^{2}\)
4. \(-125a^{8}+200a^{5}-80a^{2}\)
5. \(-3a^{5}+3a^{3}\)
6. \(-24y^{4}+54y^{2}\)
7. \(-20x^{10}+5x^{4}\)
8. \(2y^{6}-128y^{4}\)
9. \(-8p^{9}+18p^{3}\)
10. \(-20a^{8}-20a^{5}s-5a^{2}s^2\)
11. \(45p^{6}-150p^{4}s+125p^{2}s^2\)
12. \(-6p^{6}-60p^{5}-150p^{4}\)

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

Verbetersleutel

1. \(9x^{7}-49x^{5}=x^{5}(9x^{2}-49)=x^{5}(3x+7)(3x-7)\)
2. \(320p^{10}-560p^{6}x+245p^{2}x^2=5p^{2}(64p^{8}-112p^4x+49x^2)=5p^{2}(8p^4-7x)^2\)
3. \(-150q^{10}+54q^{2}=-6q^{2}(25q^{8}-9)=-6q^{2}(5q^4+3)(5q^4-3)\)
4. \(-125a^{8}+200a^{5}-80a^{2}=-5a^{2}(25a^{6}-40a^3+16)=-5a^{2}(5a^3-4)^2\)
5. \(-3a^{5}+3a^{3}=-3a^{3}(a^2-1)=-3a^{3}(a-1)(a+1)\)
6. \(-24y^{4}+54y^{2}=-6y^{2}(4y^{2}-9)=-6y^{2}(2y+3)(2y-3)\)
7. \(-20x^{10}+5x^{4}=-5x^{4}(4x^{6}-1)=-5x^{4}(2x^3+1)(2x^3-1)\)
8. \(2y^{6}-128y^{4}=2y^{4}(y^2-64)=2y^{4}(y+8)(y-8)\)
9. \(-8p^{9}+18p^{3}=-2p^{3}(4p^{6}-9)=-2p^{3}(2p^3+3)(2p^3-3)\)
10. \(-20a^{8}-20a^{5}s-5a^{2}s^2=-5a^{2}(4a^{6}+4a^3s+s^2)=-5a^{2}(2a^3+s)^2\)
11. \(45p^{6}-150p^{4}s+125p^{2}s^2=5p^{2}(9p^{4}-30p^2s+25s^2)=5p^{2}(3p^2-5s)^2\)
12. \(-6p^{6}-60p^{5}-150p^{4}=-6p^{4}(p^2+10p+25)=-6p^{4}(p+5)^2\)