Ontbinden in factoren (2)

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

1. \(27b^{16}-3b^{4}\)
2. \(108b^{6}+36b^{4}q+3b^{2}q^2\)
3. \(4y^{7}-25y^{5}\)
4. \(-147b^{10}+126b^{7}-27b^{4}\)
5. \(294p^{15}+84p^{10}q+6p^{5}q^2\)
6. \(5b^{7}-60b^{6}+180b^{5}\)
7. \(-s^{5}+36s^{3}\)
8. \(-24q^{13}+294q^{5}\)
9. \(-12s^{7}-60s^{5}-75s^{3}\)
10. \(36x^{6}-x^{4}\)
11. \(192q^{9}-336q^{6}+147q^{3}\)
12. \(-2p^{4}+50p^{2}\)

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

Verbetersleutel

1. \(27b^{16}-3b^{4}=3b^{4}(9b^{12}-1)=3b^{4}(3b^6+1)(3b^6-1)\)
2. \(108b^{6}+36b^{4}q+3b^{2}q^2=3b^{2}(36b^{4}+12b^2q+q^2)=3b^{2}(6b^2+q)^2\)
3. \(4y^{7}-25y^{5}=y^{5}(4y^{2}-25)=y^{5}(2y+5)(2y-5)\)
4. \(-147b^{10}+126b^{7}-27b^{4}=-3b^{4}(49b^{6}-42b^3+9)=-3b^{4}(7b^3-3)^2\)
5. \(294p^{15}+84p^{10}q+6p^{5}q^2=6p^{5}(49p^{10}+14p^5q+q^2)=6p^{5}(7p^5+q)^2\)
6. \(5b^{7}-60b^{6}+180b^{5}=5b^{5}(b^2-12b+36)=5b^{5}(b-6)^2\)
7. \(-s^{5}+36s^{3}=-s^{3}(s^2-36)=-s^{3}(s-6)(s+6)\)
8. \(-24q^{13}+294q^{5}=-6q^{5}(4q^{8}-49)=-6q^{5}(2q^4+7)(2q^4-7)\)
9. \(-12s^{7}-60s^{5}-75s^{3}=-3s^{3}(4s^{4}+20s^2+25)=-3s^{3}(2s^2+5)^2\)
10. \(36x^{6}-x^{4}=x^{4}(36x^{2}-1)=x^{4}(6x+1)(6x-1)\)
11. \(192q^{9}-336q^{6}+147q^{3}=3q^{3}(64q^{6}-112q^3+49)=3q^{3}(8q^3-7)^2\)
12. \(-2p^{4}+50p^{2}=-2p^{2}(p^2-25)=-2p^{2}(p+5)(p-5)\)