Ontbinden in factoren (2)

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

1. \(54x^{9}-294x^{3}\)
2. \(-150b^{15}+54b^{5}\)
3. \(-216a^{8}-360a^{6}y-150a^{4}y^2\)
4. \(294b^{9}-504b^{6}+216b^{3}\)
5. \(48q^{11}-168q^{7}x+147q^{3}x^2\)
6. \(72p^{8}-120p^{6}+50p^{4}\)
7. \(-5b^{7}+90b^{6}-405b^{5}\)
8. \(3y^{5}-108y^{3}\)
9. \(-180s^{7}+125s^{5}\)
10. \(s^{7}-25s^{5}\)
11. \(-a^{7}+9a^{5}\)
12. \(216x^{6}-294x^{4}\)

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

Verbetersleutel

1. \(54x^{9}-294x^{3}=6x^{3}(9x^{6}-49)=6x^{3}(3x^3+7)(3x^3-7)\)
2. \(-150b^{15}+54b^{5}=-6b^{5}(25b^{10}-9)=-6b^{5}(5b^5+3)(5b^5-3)\)
3. \(-216a^{8}-360a^{6}y-150a^{4}y^2=-6a^{4}(36a^{4}+60a^2y+25y^2)=-6a^{4}(6a^2+5y)^2\)
4. \(294b^{9}-504b^{6}+216b^{3}=6b^{3}(49b^{6}-84b^3+36)=6b^{3}(7b^3-6)^2\)
5. \(48q^{11}-168q^{7}x+147q^{3}x^2=3q^{3}(16q^{8}-56q^4x+49x^2)=3q^{3}(4q^4-7x)^2\)
6. \(72p^{8}-120p^{6}+50p^{4}=2p^{4}(36p^{4}-60p^2+25)=2p^{4}(6p^2-5)^2\)
7. \(-5b^{7}+90b^{6}-405b^{5}=-5b^{5}(b^2-18b+81)=-5b^{5}(b-9)^2\)
8. \(3y^{5}-108y^{3}=3y^{3}(y^2-36)=3y^{3}(y-6)(y+6)\)
9. \(-180s^{7}+125s^{5}=-5s^{5}(36s^{2}-25)=-5s^{5}(6s+5)(6s-5)\)
10. \(s^{7}-25s^{5}=s^{5}(s^2-25)=s^{5}(s+5)(s-5)\)
11. \(-a^{7}+9a^{5}=-a^{5}(a^2-9)=-a^{5}(a-3)(a+3)\)
12. \(216x^{6}-294x^{4}=6x^{4}(36x^{2}-49)=6x^{4}(6x+7)(6x-7)\)