Ontbinden in factoren (2)

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

1. \(72b^{10}+120b^{7}y+50b^{4}y^2\)
2. \(147q^{7}+42q^{6}+3q^{5}\)
3. \(-9x^{8}+49x^{4}\)
4. \(6a^{5}+24a^{4}+24a^{3}\)
5. \(-12s^{6}+75s^{4}\)
6. \(50q^{4}-2q^{2}\)
7. \(-108p^{11}-36p^{8}s-3p^{5}s^2\)
8. \(-25x^{13}-10x^{9}-x^{5}\)
9. \(150s^{4}+60s^{3}+6s^{2}\)
10. \(-150p^{12}+54p^{4}\)
11. \(-36q^{7}+25q^{5}\)
12. \(294a^{8}-504a^{6}+216a^{4}\)

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

Verbetersleutel

1. \(72b^{10}+120b^{7}y+50b^{4}y^2=2b^{4}(36b^{6}+60b^3y+25y^2)=2b^{4}(6b^3+5y)^2\)
2. \(147q^{7}+42q^{6}+3q^{5}=3q^{5}(49q^{2}+14q+1)=3q^{5}(7q+1)^2\)
3. \(-9x^{8}+49x^{4}=-x^{4}(9x^{4}-49)=-x^{4}(3x^2+7)(3x^2-7)\)
4. \(6a^{5}+24a^{4}+24a^{3}=6a^{3}(a^2+4a+4)=6a^{3}(a+2)^2\)
5. \(-12s^{6}+75s^{4}=-3s^{4}(4s^{2}-25)=-3s^{4}(2s+5)(2s-5)\)
6. \(50q^{4}-2q^{2}=2q^{2}(25q^{2}-1)=2q^{2}(5q+1)(5q-1)\)
7. \(-108p^{11}-36p^{8}s-3p^{5}s^2=-3p^{5}(36p^{6}+12p^3s+s^2)=-3p^{5}(6p^3+s)^2\)
8. \(-25x^{13}-10x^{9}-x^{5}=-x^{5}(25x^{8}+10x^4+1)=-x^{5}(5x^4+1)^2\)
9. \(150s^{4}+60s^{3}+6s^{2}=6s^{2}(25s^{2}+10s+1)=6s^{2}(5s+1)^2\)
10. \(-150p^{12}+54p^{4}=-6p^{4}(25p^{8}-9)=-6p^{4}(5p^4+3)(5p^4-3)\)
11. \(-36q^{7}+25q^{5}=-q^{5}(36q^{2}-25)=-q^{5}(6q+5)(6q-5)\)
12. \(294a^{8}-504a^{6}+216a^{4}=6a^{4}(49a^{4}-84a^2+36)=6a^{4}(7a^2-6)^2\)