Ontbinden in factoren (2)

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

1. \(12a^{7}-147a^{3}\)
2. \(b^{5}-18b^{4}+81b^{3}\)
3. \(2p^{7}+32p^{6}+128p^{5}\)
4. \(-72a^{8}+120a^{6}x-50a^{4}x^2\)
5. \(6q^{7}+108q^{6}+486q^{5}\)
6. \(-50b^{15}+2b^{3}\)
7. \(192a^{10}+48a^{7}q+3a^{4}q^2\)
8. \(-27s^{6}-36s^{4}-12s^{2}\)
9. \(-25x^{20}+36x^{4}\)
10. \(-18a^{13}+60a^{9}-50a^{5}\)
11. \(2b^{7}-98b^{5}\)
12. \(-180q^{19}+125q^{3}\)

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

Verbetersleutel

1. \(12a^{7}-147a^{3}=3a^{3}(4a^{4}-49)=3a^{3}(2a^2+7)(2a^2-7)\)
2. \(b^{5}-18b^{4}+81b^{3}=b^{3}(b^2-18b+81)=b^{3}(b-9)^2\)
3. \(2p^{7}+32p^{6}+128p^{5}=2p^{5}(p^2+16p+64)=2p^{5}(p+8)^2\)
4. \(-72a^{8}+120a^{6}x-50a^{4}x^2=-2a^{4}(36a^{4}-60a^2x+25x^2)=-2a^{4}(6a^2-5x)^2\)
5. \(6q^{7}+108q^{6}+486q^{5}=6q^{5}(q^2+18q+81)=6q^{5}(q+9)^2\)
6. \(-50b^{15}+2b^{3}=-2b^{3}(25b^{12}-1)=-2b^{3}(5b^6+1)(5b^6-1)\)
7. \(192a^{10}+48a^{7}q+3a^{4}q^2=3a^{4}(64a^{6}+16a^3q+q^2)=3a^{4}(8a^3+q)^2\)
8. \(-27s^{6}-36s^{4}-12s^{2}=-3s^{2}(9s^{4}+12s^2+4)=-3s^{2}(3s^2+2)^2\)
9. \(-25x^{20}+36x^{4}=-x^{4}(25x^{16}-36)=-x^{4}(5x^8+6)(5x^8-6)\)
10. \(-18a^{13}+60a^{9}-50a^{5}=-2a^{5}(9a^{8}-30a^4+25)=-2a^{5}(3a^4-5)^2\)
11. \(2b^{7}-98b^{5}=2b^{5}(b^2-49)=2b^{5}(b-7)(b+7)\)
12. \(-180q^{19}+125q^{3}=-5q^{3}(36q^{16}-25)=-5q^{3}(6q^8+5)(6q^8-5)\)