Ontbinden in factoren (2)

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

1. \(-32y^{19}+18y^{5}\)
2. \(-2p^{5}-28p^{4}-98p^{3}\)
3. \(-20b^{9}-20b^{7}q-5b^{5}q^2\)
4. \(-320b^{14}+560b^{9}y-245b^{4}y^2\)
5. \(72s^{11}+24s^{7}x+2s^{3}x^2\)
6. \(-8s^{7}+98s^{3}\)
7. \(-20p^{20}+125p^{4}\)
8. \(-y^{7}+18y^{6}-81y^{5}\)
9. \(75b^{10}+180b^{7}+108b^{4}\)
10. \(24q^{16}-150q^{4}\)
11. \(-3b^{5}+48b^{3}\)
12. \(50p^{6}-32p^{4}\)

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

Verbetersleutel

1. \(-32y^{19}+18y^{5}=-2y^{5}(16y^{14}-9)=-2y^{5}(4y^7+3)(4y^7-3)\)
2. \(-2p^{5}-28p^{4}-98p^{3}=-2p^{3}(p^2+14p+49)=-2p^{3}(p+7)^2\)
3. \(-20b^{9}-20b^{7}q-5b^{5}q^2=-5b^{5}(4b^{4}+4b^2q+q^2)=-5b^{5}(2b^2+q)^2\)
4. \(-320b^{14}+560b^{9}y-245b^{4}y^2=-5b^{4}(64b^{10}-112b^5y+49y^2)=-5b^{4}(8b^5-7y)^2\)
5. \(72s^{11}+24s^{7}x+2s^{3}x^2=2s^{3}(36s^{8}+12s^4x+x^2)=2s^{3}(6s^4+x)^2\)
6. \(-8s^{7}+98s^{3}=-2s^{3}(4s^{4}-49)=-2s^{3}(2s^2+7)(2s^2-7)\)
7. \(-20p^{20}+125p^{4}=-5p^{4}(4p^{16}-25)=-5p^{4}(2p^8+5)(2p^8-5)\)
8. \(-y^{7}+18y^{6}-81y^{5}=-y^{5}(y^2-18y+81)=-y^{5}(y-9)^2\)
9. \(75b^{10}+180b^{7}+108b^{4}=3b^{4}(25b^{6}+60b^3+36)=3b^{4}(5b^3+6)^2\)
10. \(24q^{16}-150q^{4}=6q^{4}(4q^{12}-25)=6q^{4}(2q^6+5)(2q^6-5)\)
11. \(-3b^{5}+48b^{3}=-3b^{3}(b^2-16)=-3b^{3}(b-4)(b+4)\)
12. \(50p^{6}-32p^{4}=2p^{4}(25p^{2}-16)=2p^{4}(5p+4)(5p-4)\)