Ontbinden in factoren (2)

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

1. \(48s^{14}-147s^{4}\)
2. \(5y^{6}-80y^{5}+320y^{4}\)
3. \(-54x^{10}-72x^{6}y-24x^{2}y^2\)
4. \(32s^{5}+112s^{4}+98s^{3}\)
5. \(-20q^{6}+125q^{4}\)
6. \(5y^{6}-125y^{4}\)
7. \(-18p^{4}+50p^{2}\)
8. \(-245b^{13}-70b^{9}q-5b^{5}q^2\)
9. \(b^{7}+8b^{6}+16b^{5}\)
10. \(48s^{6}-27s^{4}\)
11. \(36s^{20}-25s^{4}\)
12. \(125a^{14}-5a^{2}\)

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

Verbetersleutel

1. \(48s^{14}-147s^{4}=3s^{4}(16s^{10}-49)=3s^{4}(4s^5+7)(4s^5-7)\)
2. \(5y^{6}-80y^{5}+320y^{4}=5y^{4}(y^2-16y+64)=5y^{4}(y-8)^2\)
3. \(-54x^{10}-72x^{6}y-24x^{2}y^2=-6x^{2}(9x^{8}+12x^4y+4y^2)=-6x^{2}(3x^4+2y)^2\)
4. \(32s^{5}+112s^{4}+98s^{3}=2s^{3}(16s^{2}+56s+49)=2s^{3}(4s+7)^2\)
5. \(-20q^{6}+125q^{4}=-5q^{4}(4q^{2}-25)=-5q^{4}(2q+5)(2q-5)\)
6. \(5y^{6}-125y^{4}=5y^{4}(y^2-25)=5y^{4}(y-5)(y+5)\)
7. \(-18p^{4}+50p^{2}=-2p^{2}(9p^{2}-25)=-2p^{2}(3p+5)(3p-5)\)
8. \(-245b^{13}-70b^{9}q-5b^{5}q^2=-5b^{5}(49b^{8}+14b^4q+q^2)=-5b^{5}(7b^4+q)^2\)
9. \(b^{7}+8b^{6}+16b^{5}=b^{5}(b^2+8b+16)=b^{5}(b+4)^2\)
10. \(48s^{6}-27s^{4}=3s^{4}(16s^{2}-9)=3s^{4}(4s+3)(4s-3)\)
11. \(36s^{20}-25s^{4}=s^{4}(36s^{16}-25)=s^{4}(6s^8+5)(6s^8-5)\)
12. \(125a^{14}-5a^{2}=5a^{2}(25a^{12}-1)=5a^{2}(5a^6+1)(5a^6-1)\)