Ontbinden in factoren (2)

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

1. \(4a^{14}+4a^{9}b+a^{4}b^2\)
2. \(96b^{7}-150b^{5}\)
3. \(-8s^{4}-8s^{3}-2s^{2}\)
4. \(-6x^{4}+108x^{3}-486x^{2}\)
5. \(-192q^{7}+336q^{5}-147q^{3}\)
6. \(-180q^{4}+5q^{2}\)
7. \(216q^{5}+72q^{4}+6q^{3}\)
8. \(p^{4}-64p^{2}\)
9. \(-24p^{6}-72p^{4}y-54p^{2}y^2\)
10. \(6a^{4}+24a^{3}+24a^{2}\)
11. \(4q^{12}+4q^{8}+q^{4}\)
12. \(108a^{12}-180a^{7}y+75a^{2}y^2\)

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

Verbetersleutel

1. \(4a^{14}+4a^{9}b+a^{4}b^2=a^{4}(4a^{10}+4a^5b+b^2)=a^{4}(2a^5+b)^2\)
2. \(96b^{7}-150b^{5}=6b^{5}(16b^{2}-25)=6b^{5}(4b+5)(4b-5)\)
3. \(-8s^{4}-8s^{3}-2s^{2}=-2s^{2}(4s^{2}+4s+1)=-2s^{2}(2s+1)^2\)
4. \(-6x^{4}+108x^{3}-486x^{2}=-6x^{2}(x^2-18x+81)=-6x^{2}(x-9)^2\)
5. \(-192q^{7}+336q^{5}-147q^{3}=-3q^{3}(64q^{4}-112q^2+49)=-3q^{3}(8q^2-7)^2\)
6. \(-180q^{4}+5q^{2}=-5q^{2}(36q^{2}-1)=-5q^{2}(6q+1)(6q-1)\)
7. \(216q^{5}+72q^{4}+6q^{3}=6q^{3}(36q^{2}+12q+1)=6q^{3}(6q+1)^2\)
8. \(p^{4}-64p^{2}=p^{2}(p^2-64)=p^{2}(p-8)(p+8)\)
9. \(-24p^{6}-72p^{4}y-54p^{2}y^2=-6p^{2}(4p^{4}+12p^2y+9y^2)=-6p^{2}(2p^2+3y)^2\)
10. \(6a^{4}+24a^{3}+24a^{2}=6a^{2}(a^2+4a+4)=6a^{2}(a+2)^2\)
11. \(4q^{12}+4q^{8}+q^{4}=q^{4}(4q^{8}+4q^4+1)=q^{4}(2q^4+1)^2\)
12. \(108a^{12}-180a^{7}y+75a^{2}y^2=3a^{2}(36a^{10}-60a^5y+25y^2)=3a^{2}(6a^5-5y)^2\)