Ontbinden in factoren (2)

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

1. \(18a^{13}-60a^{9}x+50a^{5}x^2\)
2. \(-2q^{4}+20q^{3}-50q^{2}\)
3. \(-20y^{12}+125y^{4}\)
4. \(-p^{5}+8p^{4}-16p^{3}\)
5. \(18p^{7}-24p^{6}+8p^{5}\)
6. \(54s^{18}-6s^{4}\)
7. \(-6q^{6}+6q^{4}\)
8. \(20b^{6}+20b^{4}p+5b^{2}p^2\)
9. \(5b^{7}-5b^{5}\)
10. \(20y^{5}-125y^{3}\)
11. \(x^{7}-36x^{5}\)
12. \(150s^{21}-294s^{5}\)

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

Verbetersleutel

1. \(18a^{13}-60a^{9}x+50a^{5}x^2=2a^{5}(9a^{8}-30a^4x+25x^2)=2a^{5}(3a^4-5x)^2\)
2. \(-2q^{4}+20q^{3}-50q^{2}=-2q^{2}(q^2-10q+25)=-2q^{2}(q-5)^2\)
3. \(-20y^{12}+125y^{4}=-5y^{4}(4y^{8}-25)=-5y^{4}(2y^4+5)(2y^4-5)\)
4. \(-p^{5}+8p^{4}-16p^{3}=-p^{3}(p^2-8p+16)=-p^{3}(p-4)^2\)
5. \(18p^{7}-24p^{6}+8p^{5}=2p^{5}(9p^{2}-12p+4)=2p^{5}(3p-2)^2\)
6. \(54s^{18}-6s^{4}=6s^{4}(9s^{14}-1)=6s^{4}(3s^7+1)(3s^7-1)\)
7. \(-6q^{6}+6q^{4}=-6q^{4}(q^2-1)=-6q^{4}(q-1)(q+1)\)
8. \(20b^{6}+20b^{4}p+5b^{2}p^2=5b^{2}(4b^{4}+4b^2p+p^2)=5b^{2}(2b^2+p)^2\)
9. \(5b^{7}-5b^{5}=5b^{5}(b^2-1)=5b^{5}(b-1)(b+1)\)
10. \(20y^{5}-125y^{3}=5y^{3}(4y^{2}-25)=5y^{3}(2y+5)(2y-5)\)
11. \(x^{7}-36x^{5}=x^{5}(x^2-36)=x^{5}(x-6)(x+6)\)
12. \(150s^{21}-294s^{5}=6s^{5}(25s^{16}-49)=6s^{5}(5s^8+7)(5s^8-7)\)