Ontbinden in factoren (2)

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

1. \(-16a^{12}+24a^{8}y-9a^{4}y^2\)
2. \(180b^{6}+60b^{5}+5b^{4}\)
3. \(25q^{7}+60q^{6}+36q^{5}\)
4. \(5y^{6}-320y^{4}\)
5. \(24s^{6}-54s^{4}\)
6. \(-180b^{7}-300b^{5}-125b^{3}\)
7. \(-5y^{6}-70y^{5}-245y^{4}\)
8. \(p^{7}+10p^{6}+25p^{5}\)
9. \(-3b^{5}-18b^{4}-27b^{3}\)
10. \(3s^{6}-48s^{4}\)
11. \(-2y^{4}+8y^{3}-8y^{2}\)
12. \(25s^{10}+40s^{6}+16s^{2}\)

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

Verbetersleutel

1. \(-16a^{12}+24a^{8}y-9a^{4}y^2=-a^{4}(16a^{8}-24a^4y+9y^2)=-a^{4}(4a^4-3y)^2\)
2. \(180b^{6}+60b^{5}+5b^{4}=5b^{4}(36b^{2}+12b+1)=5b^{4}(6b+1)^2\)
3. \(25q^{7}+60q^{6}+36q^{5}=q^{5}(25q^{2}+60q+36)=q^{5}(5q+6)^2\)
4. \(5y^{6}-320y^{4}=5y^{4}(y^2-64)=5y^{4}(y-8)(y+8)\)
5. \(24s^{6}-54s^{4}=6s^{4}(4s^{2}-9)=6s^{4}(2s+3)(2s-3)\)
6. \(-180b^{7}-300b^{5}-125b^{3}=-5b^{3}(36b^{4}+60b^2+25)=-5b^{3}(6b^2+5)^2\)
7. \(-5y^{6}-70y^{5}-245y^{4}=-5y^{4}(y^2+14y+49)=-5y^{4}(y+7)^2\)
8. \(p^{7}+10p^{6}+25p^{5}=p^{5}(p^2+10p+25)=p^{5}(p+5)^2\)
9. \(-3b^{5}-18b^{4}-27b^{3}=-3b^{3}(b^2+6b+9)=-3b^{3}(b+3)^2\)
10. \(3s^{6}-48s^{4}=3s^{4}(s^2-16)=3s^{4}(s+4)(s-4)\)
11. \(-2y^{4}+8y^{3}-8y^{2}=-2y^{2}(y^2-4y+4)=-2y^{2}(y-2)^2\)
12. \(25s^{10}+40s^{6}+16s^{2}=s^{2}(25s^{8}+40s^4+16)=s^{2}(5s^4+4)^2\)