Ontbinden in factoren (2)

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

1. \(6s^{7}-216s^{5}\)
2. \(27b^{13}-36b^{9}x+12b^{5}x^2\)
3. \(24x^{7}-294x^{5}\)
4. \(s^{7}-64s^{5}\)
5. \(32p^{5}-112p^{4}+98p^{3}\)
6. \(49a^{6}-42a^{4}p+9a^{2}p^2\)
7. \(49q^{7}-84q^{5}x+36q^{3}x^2\)
8. \(96p^{5}-150p^{3}\)
9. \(-54p^{21}+96p^{5}\)
10. \(-294x^{9}-336x^{7}y-96x^{5}y^2\)
11. \(75p^{11}+30p^{8}+3p^{5}\)
12. \(-20a^{17}+245a^{3}\)

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

Verbetersleutel

1. \(6s^{7}-216s^{5}=6s^{5}(s^2-36)=6s^{5}(s+6)(s-6)\)
2. \(27b^{13}-36b^{9}x+12b^{5}x^2=3b^{5}(9b^{8}-12b^4x+4x^2)=3b^{5}(3b^4-2x)^2\)
3. \(24x^{7}-294x^{5}=6x^{5}(4x^{2}-49)=6x^{5}(2x+7)(2x-7)\)
4. \(s^{7}-64s^{5}=s^{5}(s^2-64)=s^{5}(s-8)(s+8)\)
5. \(32p^{5}-112p^{4}+98p^{3}=2p^{3}(16p^{2}-56p+49)=2p^{3}(4p-7)^2\)
6. \(49a^{6}-42a^{4}p+9a^{2}p^2=a^{2}(49a^{4}-42a^2p+9p^2)=a^{2}(7a^2-3p)^2\)
7. \(49q^{7}-84q^{5}x+36q^{3}x^2=q^{3}(49q^{4}-84q^2x+36x^2)=q^{3}(7q^2-6x)^2\)
8. \(96p^{5}-150p^{3}=6p^{3}(16p^{2}-25)=6p^{3}(4p+5)(4p-5)\)
9. \(-54p^{21}+96p^{5}=-6p^{5}(9p^{16}-16)=-6p^{5}(3p^8+4)(3p^8-4)\)
10. \(-294x^{9}-336x^{7}y-96x^{5}y^2=-6x^{5}(49x^{4}+56x^2y+16y^2)=-6x^{5}(7x^2+4y)^2\)
11. \(75p^{11}+30p^{8}+3p^{5}=3p^{5}(25p^{6}+10p^3+1)=3p^{5}(5p^3+1)^2\)
12. \(-20a^{17}+245a^{3}=-5a^{3}(4a^{14}-49)=-5a^{3}(2a^7+7)(2a^7-7)\)