Ontbinden in factoren (2)

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

1. \(3s^{7}-27s^{5}\)
2. \(36a^{12}+60a^{7}+25a^{2}\)
3. \(-18b^{12}+24b^{7}p-8b^{2}p^2\)
4. \(-2b^{4}+18b^{2}\)
5. \(-12b^{14}-12b^{9}p-3b^{4}p^2\)
6. \(6a^{7}+72a^{6}+216a^{5}\)
7. \(-20b^{12}-20b^{7}-5b^{2}\)
8. \(-b^{4}+49b^{2}\)
9. \(-80a^{7}-40a^{5}x-5a^{3}x^2\)
10. \(-b^{4}+4b^{2}\)
11. \(-180q^{7}-300q^{5}s-125q^{3}s^2\)
12. \(-8a^{6}-40a^{5}-50a^{4}\)

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

Verbetersleutel

1. \(3s^{7}-27s^{5}=3s^{5}(s^2-9)=3s^{5}(s-3)(s+3)\)
2. \(36a^{12}+60a^{7}+25a^{2}=a^{2}(36a^{10}+60a^5+25)=a^{2}(6a^5+5)^2\)
3. \(-18b^{12}+24b^{7}p-8b^{2}p^2=-2b^{2}(9b^{10}-12b^5p+4p^2)=-2b^{2}(3b^5-2p)^2\)
4. \(-2b^{4}+18b^{2}=-2b^{2}(b^2-9)=-2b^{2}(b+3)(b-3)\)
5. \(-12b^{14}-12b^{9}p-3b^{4}p^2=-3b^{4}(4b^{10}+4b^5p+p^2)=-3b^{4}(2b^5+p)^2\)
6. \(6a^{7}+72a^{6}+216a^{5}=6a^{5}(a^2+12a+36)=6a^{5}(a+6)^2\)
7. \(-20b^{12}-20b^{7}-5b^{2}=-5b^{2}(4b^{10}+4b^5+1)=-5b^{2}(2b^5+1)^2\)
8. \(-b^{4}+49b^{2}=-b^{2}(b^2-49)=-b^{2}(b+7)(b-7)\)
9. \(-80a^{7}-40a^{5}x-5a^{3}x^2=-5a^{3}(16a^{4}+8a^2x+x^2)=-5a^{3}(4a^2+x)^2\)
10. \(-b^{4}+4b^{2}=-b^{2}(b^2-4)=-b^{2}(b-2)(b+2)\)
11. \(-180q^{7}-300q^{5}s-125q^{3}s^2=-5q^{3}(36q^{4}+60q^2s+25s^2)=-5q^{3}(6q^2+5s)^2\)
12. \(-8a^{6}-40a^{5}-50a^{4}=-2a^{4}(4a^{2}+20a+25)=-2a^{4}(2a+5)^2\)