Ontbinden in factoren (2)

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

1. \(16b^{10}-b^{4}\)
2. \(-32a^{6}+18a^{4}\)
3. \(12q^{4}-3q^{2}\)
4. \(5q^{6}-245q^{4}\)
5. \(3q^{7}+12q^{6}+12q^{5}\)
6. \(-32s^{6}+98s^{4}\)
7. \(5a^{7}-320a^{5}\)
8. \(45q^{8}+120q^{6}x+80q^{4}x^2\)
9. \(125a^{4}-450a^{3}+405a^{2}\)
10. \(-98b^{12}-140b^{7}x-50b^{2}x^2\)
11. \(-48b^{15}+168b^{10}y-147b^{5}y^2\)
12. \(32s^{4}+16s^{3}+2s^{2}\)

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

Verbetersleutel

1. \(16b^{10}-b^{4}=b^{4}(16b^{6}-1)=b^{4}(4b^3+1)(4b^3-1)\)
2. \(-32a^{6}+18a^{4}=-2a^{4}(16a^{2}-9)=-2a^{4}(4a+3)(4a-3)\)
3. \(12q^{4}-3q^{2}=3q^{2}(4q^{2}-1)=3q^{2}(2q+1)(2q-1)\)
4. \(5q^{6}-245q^{4}=5q^{4}(q^2-49)=5q^{4}(q-7)(q+7)\)
5. \(3q^{7}+12q^{6}+12q^{5}=3q^{5}(q^2+4q+4)=3q^{5}(q+2)^2\)
6. \(-32s^{6}+98s^{4}=-2s^{4}(16s^{2}-49)=-2s^{4}(4s+7)(4s-7)\)
7. \(5a^{7}-320a^{5}=5a^{5}(a^2-64)=5a^{5}(a+8)(a-8)\)
8. \(45q^{8}+120q^{6}x+80q^{4}x^2=5q^{4}(9q^{4}+24q^2x+16x^2)=5q^{4}(3q^2+4x)^2\)
9. \(125a^{4}-450a^{3}+405a^{2}=5a^{2}(25a^{2}-90a+81)=5a^{2}(5a-9)^2\)
10. \(-98b^{12}-140b^{7}x-50b^{2}x^2=-2b^{2}(49b^{10}+70b^5x+25x^2)=-2b^{2}(7b^5+5x)^2\)
11. \(-48b^{15}+168b^{10}y-147b^{5}y^2=-3b^{5}(16b^{10}-56b^5y+49y^2)=-3b^{5}(4b^5-7y)^2\)
12. \(32s^{4}+16s^{3}+2s^{2}=2s^{2}(16s^{2}+8s+1)=2s^{2}(4s+1)^2\)