Ontbinden in factoren (2)

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

1. \(-36b^{14}+25b^{4}\)
2. \(-8b^{19}+2b^{5}\)
3. \(-180b^{9}-60b^{7}-5b^{5}\)
4. \(-5y^{5}+5y^{3}\)
5. \(180a^{18}-125a^{2}\)
6. \(45q^{6}-150q^{4}+125q^{2}\)
7. \(-36a^{12}-60a^{7}-25a^{2}\)
8. \(q^{6}-q^{4}\)
9. \(4b^{5}+20b^{4}+25b^{3}\)
10. \(32y^{14}-98y^{2}\)
11. \(-384a^{5}+672a^{4}-294a^{3}\)
12. \(-294x^{12}+252x^{7}-54x^{2}\)

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

Verbetersleutel

1. \(-36b^{14}+25b^{4}=-b^{4}(36b^{10}-25)=-b^{4}(6b^5+5)(6b^5-5)\)
2. \(-8b^{19}+2b^{5}=-2b^{5}(4b^{14}-1)=-2b^{5}(2b^7+1)(2b^7-1)\)
3. \(-180b^{9}-60b^{7}-5b^{5}=-5b^{5}(36b^{4}+12b^2+1)=-5b^{5}(6b^2+1)^2\)
4. \(-5y^{5}+5y^{3}=-5y^{3}(y^2-1)=-5y^{3}(y+1)(y-1)\)
5. \(180a^{18}-125a^{2}=5a^{2}(36a^{16}-25)=5a^{2}(6a^8+5)(6a^8-5)\)
6. \(45q^{6}-150q^{4}+125q^{2}=5q^{2}(9q^{4}-30q^2+25)=5q^{2}(3q^2-5)^2\)
7. \(-36a^{12}-60a^{7}-25a^{2}=-a^{2}(36a^{10}+60a^5+25)=-a^{2}(6a^5+5)^2\)
8. \(q^{6}-q^{4}=q^{4}(q^2-1)=q^{4}(q+1)(q-1)\)
9. \(4b^{5}+20b^{4}+25b^{3}=b^{3}(4b^{2}+20b+25)=b^{3}(2b+5)^2\)
10. \(32y^{14}-98y^{2}=2y^{2}(16y^{12}-49)=2y^{2}(4y^6+7)(4y^6-7)\)
11. \(-384a^{5}+672a^{4}-294a^{3}=-6a^{3}(64a^{2}-112a+49)=-6a^{3}(8a-7)^2\)
12. \(-294x^{12}+252x^{7}-54x^{2}=-6x^{2}(49x^{10}-42x^5+9)=-6x^{2}(7x^5-3)^2\)