Ontbinden in factoren (2)

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

1. \(-96b^{13}+294b^{5}\)
2. \(108p^{13}+36p^{8}y+3p^{3}y^2\)
3. \(9s^{21}-49s^{5}\)
4. \(18s^{10}+12s^{7}y+2s^{4}y^2\)
5. \(-192y^{13}+336y^{9}-147y^{5}\)
6. \(125b^{12}-200b^{8}p+80b^{4}p^2\)
7. \(72q^{6}-120q^{5}+50q^{4}\)
8. \(-27s^{5}+12s^{3}\)
9. \(-12a^{12}-12a^{7}-3a^{2}\)
10. \(-5x^{5}+180x^{3}\)
11. \(72q^{16}-50q^{4}\)
12. \(-s^{6}-12s^{5}-36s^{4}\)

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

Verbetersleutel

1. \(-96b^{13}+294b^{5}=-6b^{5}(16b^{8}-49)=-6b^{5}(4b^4+7)(4b^4-7)\)
2. \(108p^{13}+36p^{8}y+3p^{3}y^2=3p^{3}(36p^{10}+12p^5y+y^2)=3p^{3}(6p^5+y)^2\)
3. \(9s^{21}-49s^{5}=s^{5}(9s^{16}-49)=s^{5}(3s^8+7)(3s^8-7)\)
4. \(18s^{10}+12s^{7}y+2s^{4}y^2=2s^{4}(9s^{6}+6s^3y+y^2)=2s^{4}(3s^3+y)^2\)
5. \(-192y^{13}+336y^{9}-147y^{5}=-3y^{5}(64y^{8}-112y^4+49)=-3y^{5}(8y^4-7)^2\)
6. \(125b^{12}-200b^{8}p+80b^{4}p^2=5b^{4}(25b^{8}-40b^4p+16p^2)=5b^{4}(5b^4-4p)^2\)
7. \(72q^{6}-120q^{5}+50q^{4}=2q^{4}(36q^{2}-60q+25)=2q^{4}(6q-5)^2\)
8. \(-27s^{5}+12s^{3}=-3s^{3}(9s^{2}-4)=-3s^{3}(3s+2)(3s-2)\)
9. \(-12a^{12}-12a^{7}-3a^{2}=-3a^{2}(4a^{10}+4a^5+1)=-3a^{2}(2a^5+1)^2\)
10. \(-5x^{5}+180x^{3}=-5x^{3}(x^2-36)=-5x^{3}(x+6)(x-6)\)
11. \(72q^{16}-50q^{4}=2q^{4}(36q^{12}-25)=2q^{4}(6q^6+5)(6q^6-5)\)
12. \(-s^{6}-12s^{5}-36s^{4}=-s^{4}(s^2+12s+36)=-s^{4}(s+6)^2\)