Ontbinden in factoren (2)

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

1. \(-48b^{9}+168b^{7}y-147b^{5}y^2\)
2. \(-4s^{6}-4s^{5}-s^{4}\)
3. \(48a^{17}-147a^{3}\)
4. \(9b^{4}+12b^{3}+4b^{2}\)
5. \(25a^{14}+40a^{9}x+16a^{4}x^2\)
6. \(-9p^{18}+16p^{4}\)
7. \(x^{6}-36x^{4}\)
8. \(80p^{9}-280p^{6}q+245p^{3}q^2\)
9. \(-54p^{6}-144p^{5}-96p^{4}\)
10. \(64a^{10}+16a^{6}x+a^{2}x^2\)
11. \(-2q^{4}+128q^{2}\)
12. \(36q^{18}-q^{2}\)

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

Verbetersleutel

1. \(-48b^{9}+168b^{7}y-147b^{5}y^2=-3b^{5}(16b^{4}-56b^2y+49y^2)=-3b^{5}(4b^2-7y)^2\)
2. \(-4s^{6}-4s^{5}-s^{4}=-s^{4}(4s^{2}+4s+1)=-s^{4}(2s+1)^2\)
3. \(48a^{17}-147a^{3}=3a^{3}(16a^{14}-49)=3a^{3}(4a^7+7)(4a^7-7)\)
4. \(9b^{4}+12b^{3}+4b^{2}=b^{2}(9b^{2}+12b+4)=b^{2}(3b+2)^2\)
5. \(25a^{14}+40a^{9}x+16a^{4}x^2=a^{4}(25a^{10}+40a^5x+16x^2)=a^{4}(5a^5+4x)^2\)
6. \(-9p^{18}+16p^{4}=-p^{4}(9p^{14}-16)=-p^{4}(3p^7+4)(3p^7-4)\)
7. \(x^{6}-36x^{4}=x^{4}(x^2-36)=x^{4}(x+6)(x-6)\)
8. \(80p^{9}-280p^{6}q+245p^{3}q^2=5p^{3}(16p^{6}-56p^3q+49q^2)=5p^{3}(4p^3-7q)^2\)
9. \(-54p^{6}-144p^{5}-96p^{4}=-6p^{4}(9p^{2}+24p+16)=-6p^{4}(3p+4)^2\)
10. \(64a^{10}+16a^{6}x+a^{2}x^2=a^{2}(64a^{8}+16a^4x+x^2)=a^{2}(8a^4+x)^2\)
11. \(-2q^{4}+128q^{2}=-2q^{2}(q^2-64)=-2q^{2}(q+8)(q-8)\)
12. \(36q^{18}-q^{2}=q^{2}(36q^{16}-1)=q^{2}(6q^8+1)(6q^8-1)\)