Ontbinden in factoren (2)

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

1. \(4a^{14}+4a^{9}y+a^{4}y^2\)
2. \(-96p^{10}+144p^{7}q-54p^{4}q^2\)
3. \(-q^{7}+9q^{5}\)
4. \(24x^{14}-54x^{4}\)
5. \(-384b^{11}-96b^{7}-6b^{3}\)
6. \(-a^{7}-12a^{6}-36a^{5}\)
7. \(32x^{14}-18x^{2}\)
8. \(6p^{6}-72p^{5}+216p^{4}\)
9. \(6x^{4}-84x^{3}+294x^{2}\)
10. \(16b^{7}-24b^{6}+9b^{5}\)
11. \(6y^{5}-96y^{3}\)
12. \(36s^{7}+12s^{6}+s^{5}\)

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

Verbetersleutel

1. \(4a^{14}+4a^{9}y+a^{4}y^2=a^{4}(4a^{10}+4a^5y+y^2)=a^{4}(2a^5+y)^2\)
2. \(-96p^{10}+144p^{7}q-54p^{4}q^2=-6p^{4}(16p^{6}-24p^3q+9q^2)=-6p^{4}(4p^3-3q)^2\)
3. \(-q^{7}+9q^{5}=-q^{5}(q^2-9)=-q^{5}(q+3)(q-3)\)
4. \(24x^{14}-54x^{4}=6x^{4}(4x^{10}-9)=6x^{4}(2x^5+3)(2x^5-3)\)
5. \(-384b^{11}-96b^{7}-6b^{3}=-6b^{3}(64b^{8}+16b^4+1)=-6b^{3}(8b^4+1)^2\)
6. \(-a^{7}-12a^{6}-36a^{5}=-a^{5}(a^2+12a+36)=-a^{5}(a+6)^2\)
7. \(32x^{14}-18x^{2}=2x^{2}(16x^{12}-9)=2x^{2}(4x^6+3)(4x^6-3)\)
8. \(6p^{6}-72p^{5}+216p^{4}=6p^{4}(p^2-12p+36)=6p^{4}(p-6)^2\)
9. \(6x^{4}-84x^{3}+294x^{2}=6x^{2}(x^2-14x+49)=6x^{2}(x-7)^2\)
10. \(16b^{7}-24b^{6}+9b^{5}=b^{5}(16b^{2}-24b+9)=b^{5}(4b-3)^2\)
11. \(6y^{5}-96y^{3}=6y^{3}(y^2-16)=6y^{3}(y-4)(y+4)\)
12. \(36s^{7}+12s^{6}+s^{5}=s^{5}(36s^{2}+12s+1)=s^{5}(6s+1)^2\)